{"id":265182,"date":"2023-10-24T09:00:00","date_gmt":"2023-10-24T07:00:00","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=265182"},"modified":"2024-04-15T18:53:00","modified_gmt":"2024-04-15T16:53:00","slug":"calculs-litteraux","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/calculs-litteraux\/","title":{"rendered":"Calculs litt\u00e9raux : un monde sans chiffres \ud83d\ude2f !\u00a0"},"content":{"rendered":"\n<p>Toi qui pensais que les math\u00e9matiques n&#8217;\u00e9taient que des calculs avec des chiffres et des nombres, d\u00e9sol\u00e9 de te dire que ce n\u2019est pas exactement le cas.&nbsp;<\/p>\n\n\n\n<p>On va voir aujourd&#8217;hui que <strong>les lettres se tapent l\u2019incruste dans tes cours de maths<\/strong>. Et oui, tu les utilises pour <a href=\"https:\/\/sherpas.com\/blog\/comment-faire-une-bonne-dissertation\/\">\u00e9crire ta meilleure r\u00e9daction de fran\u00e7ais<\/a> d\u2019habitude, mais l\u00e0, elles vont se retrouver dans tes \u00e9quations. C\u2019\u00e9tait d\u00e9j\u00e0 bien assez compliqu\u00e9 avec des nombres, tu me diras \ud83d\ude21.&nbsp;<\/p>\n\n\n\n<p>Allez, ne te d\u00e9courage pas ! Prends ta calculatrice et suis les Sherpas dans un monde o\u00f9 une lettre peut se compter.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Des chiffres et des lettres \ud83d\udd22\ud83d\udd20<\/h2>\n\n\n\n<p>Le monde des math\u00e9matiques est vaste et complexe et pour cela, il a fallu que l\u2019homme invente les chiffres, puis qu\u2019il se dise que, finalement, ajouter une lettre dans un calcul et bah ce n&#8217;est pas si mal que \u00e7a. Et \u00e0 l&#8217;expression litt\u00e9rale et aux calculs litt\u00e9raux de na\u00eetre. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">D\u00e9finitions et origine \u2712\ufe0f<\/h3>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 D\u00e9finition<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Une expression litt\u00e9rale est <\/span><b>une expression math\u00e9matique contenant une ou plusieurs lettres qui d\u00e9signent des nombres<\/b><span style=\"font-weight: 400\">.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">Le \u00ab calcul litt\u00e9ral \u00bb signifie \u00ab calcul avec des lettres \u00bb. Cela englobe de nombreuses \u00e9quations et in\u00e9quations.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p><strong>L&#8217;alg\u00e8bre a fait des progr\u00e8s prodigieux <\/strong>gr\u00e2ce aux math\u00e9maticiens fran\u00e7ais Fran\u00e7ois Vi\u00e8te (1540-1603) et Albert Girard (1595-1632) \ud83e\uddd1\u200d\ud83d\udd2c.<\/p>\n\n\n\n<p>Au lieu d&#8217;exprimer les solutions \u00e0 des probl\u00e8mes math\u00e9matiques en langage courant, ils utilis\u00e8rent dans un premier temps des chiffres. Jusque-l\u00e0, \u00e7a ne semble pas si fou. Mais leur plus brillante id\u00e9e a \u00e9t\u00e9 <strong>d&#8217;utiliser des lettres pour d\u00e9signer des valeurs donn\u00e9es et des inconnues \ud83d\udc4f<\/strong>.<\/p>\n\n\n\n<p>Ainsi, un \u00e9nonc\u00e9 tel que : \u00ab Trouver un nombre dont le triple ajout\u00e9 au nombre quatre vaut z\u00e9ro \u00bb est devenu : \u00ab R\u00e9soudre 3x + 4 = 0 \u00bb. Un probl\u00e8me qui n\u00e9cessitait jadis plusieurs pages, se r\u00e9sout d\u00e9sormais en quelques ligne de calculs.<\/p>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p>Si tu penses qu\u2019elles ne servent pas \u00e0 grand-chose, voici <a href=\"https:\/\/sherpas.com\/blog\/utiliser-maths-vie-courante\/\">9 fa\u00e7ons d\u2019utiliser les maths dans la vie courante !<\/a> \ud83d\udc46<\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\">Le penseur du calcul litt\u00e9ral \ud83d\udd0d<\/h3>\n\n\n\n<p>C&#8217;est en 1571 et 1591 que Fran\u00e7ois Vi\u00e8te (1540-1603) publie deux ouvrages ouvrage sur la trigonom\u00e9trie (<em>Canon mathematicus<\/em> et <em>In artem analyticem isagoge<\/em>), qui repr\u00e9sentent un grand pas en avant pour l\u2019alg\u00e8bre. Pour Vi\u00e8te, <strong>le calcul litt\u00e9ral a pour but clair de r\u00e9soudre tous les probl\u00e8mes<\/strong>. Les inconnues sont donc d\u00e9sign\u00e9es par des voyelles et les grandeurs connues par des consonnes \ud83d\udd21.&nbsp;<\/p>\n\n\n\n<p>Sacr\u00e9 Fran\u00e7ois ! Allez, voyons comment les calculs litt\u00e9raux fonctionnent maintenant.&nbsp;<\/p>\n\n\n<section class=\"relance\">\n        <div >\n                            <a  href=\"https:\/\/sherpas.com\/cours\/maths\">\n                    <div class=\"relance__container\"\n                        >\n                        \n                                                        <picture>\n                            <source srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-4.jpg\" media=\"(min-width: 999px)\">\n                            <source srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-4.jpg\" media=\"(max-width: 999px)\">\n                                <img decoding=\"async\"\n                                    src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-4.jpg\"\n                                    alt=\"Personne qui donne des cours particuliers\"\n                                >\n                            <\/picture>\n                                                <div class=\"relance__content\">\n                            \n                                <div class=\"relance__title\"> <p>Tu gal\u00e8res en maths ? Trouve ton prof particulier chez les Sherpas !<\/p>\n<\/div>\n                                                        <button type=\"button\"\n                                    class=\"relance__button btn btn-white\">\n                                Trouve ton prof de maths !\n                            <\/button>\n                        <\/div>\n                    <\/div>\n                <\/a>\n                    <\/div>\n    <\/section>\n\n    \n\n\n<h2 class=\"wp-block-heading\">L\u2019introduction aux calculs litt\u00e9raux \u2604\ufe0f<\/h2>\n\n\n\n<p>Voici la formule de base du calcul litt\u00e9ral : ka + kb = k(a+b) ou (a+b)k. Ne sois pas effray\u00e9, on va t\u2019expliquer au mieux pour que<strong> tu ressortes de cet article en ayant tout compris<\/strong> !<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">&nbsp;La distributivit\u00e9 \ud83d\udc49 <\/h3>\n\n\n\n<p>On va d\u00e9tailler un peu plus cette formule : k \u00d7 (a + b) = k \u00d7 a + k \u00d7 b ; soit k(a + b) = ka + kb. C\u2019est le m\u00eame principe pour la soustraction : k \u00d7 (a &#8211; b) = k \u00d7 a \u2212 k \u00d7 b ; soit k(a &#8211; b) = ka &#8211; kb.<\/p>\n\n\n\n<p>C\u2019est bon tu commence \u00e0 saisir ?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/rKxEIq5DnszGsWHGZn\/giphy.gif\" alt=\"Personnage de dessin anim\u00e9 qui est perdu\"\/><\/figure><\/div>\n\n\n<p>Cest ce qu&#8217;on nomme la \u00ab distributivit\u00e9 \u00bb, car <strong>en d\u00e9veloppant l\u2019expression, on \u00ab distribue les lettres sur les autres \u00bb<\/strong>.<\/p>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p>Si tu es f\u00e2ch\u00e9 avec les multiplications, on t\u2019invite \u00e0 <a href=\"https:\/\/sherpas.com\/blog\/apprendre-les-tables-de-multiplication-par-coeur\/\">apprendre tes tables comme par magie \ud83e\uddd9!\u00a0<\/a><\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h4 class=\"wp-block-heading\">Le d\u00e9veloppement \ud83d\ude42<\/h4>\n\n\n\n<p>D\u00e9velopper signifie que l&#8217;on <strong>transforme une multiplication en une somme ou en une diff\u00e9rence<\/strong>.<\/p>\n\n\n\n<p>Dans les formules pr\u00e9c\u00e9dentes, on a transform\u00e9 le produit de k par (a + b) (ou (a \u2212b)) en une somme (ou une diff\u00e9rence). Donc : k \u00d7 (a + b) et k \u00d7 (a \u2212 b), sont devenus : ka + kb et ka &#8211; kb.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1Exemple<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">D\u00e9velopper l\u2019expression 3(4x &#8211; 6).<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">D\u2019apr\u00e8s les formules de distributivit\u00e9, on a : 3(4x &#8211; 6) = 3 \u00d7 4x &#8211; 3 \u00d7 6 = 12x &#8211; 18.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<h4 class=\"wp-block-heading\">La factorisation \ud83e\udd0f<\/h4>\n\n\n\n<p>En revanche, <strong>factoriser signifie faire le chemin inverse : une somme ou une diff\u00e9rence devient un produit<\/strong>. Si on reprend l\u2019exemple de tout \u00e0 l\u2019heure, mais que l&#8217;on factorise au lieu de d\u00e9velopper, on peut passer de &#8220;k \u00d7 a + k \u00d7 b ou k \u00d7 a &#8211; k \u00d7 b&#8221; aux formes factoris\u00e9es que sont  &#8220;k(a+b) et k(a-b)&#8221;.<\/p>\n\n\n\n<p>La <a href=\"https:\/\/sherpas.com\/blog\/factorisation\/\">factorisation<\/a>, comme tu peux le voir, simplifie l\u2019expression math\u00e9matique, c\u2019est-\u00e0-dire qu&#8217;elle permet de <strong>trouver un facteur commun \u00e0 a et b<\/strong>.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 Exemples<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Factorisons par x l\u2019expression 5x + 8x.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><span style=\"font-weight: 400\">5x + 8x = x(5 + 8) = 13x.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">On va ajouter quelques lettres et on va maintenant factoriser l\u2019expression 4a + 3b &#8211; 8a + 6b. <\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><span style=\"font-weight: 400\">4a + 3b &#8211; 8a + 6b = 4a &#8211; 8a + 3b + 6b = a(4 &#8211; 8) + b(3 + 6) = &#8211; 4a + 9b.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<h3 class=\"wp-block-heading\">La double distributivit\u00e9 \u203c\ufe0f<\/h3>\n\n\n\n<p>La double distributivit\u00e9 porte bien son nom et signifie qu\u2019il faut juste que <strong>tu distribues deux fois et pas une \ud83d\udc4d<\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/3oFzlUThksB7Atw3L2\/giphy.gif\" alt=\"Personne qui te fait comprendre que c'est logique\"\/><figcaption class=\"wp-element-caption\">Logique !<\/figcaption><\/figure><\/div>\n\n\n<p>On s\u2019en sert pour les expressions du style :&nbsp;(a + b) (c + d) tel que a, b, c et d sont des <a href=\"https:\/\/sherpas.com\/blog\/nombre-relatif\/\" data-type=\"post\" data-id=\"254000\">nombres relatifs<\/a> (entiers positifs ou n\u00e9gatifs). On distribue donc \u00ab a \u00bb sur \u00ab c \u00bb et \u00ab d \u00bb ; et \u00ab b \u00bb sur \u00ab c \u00bb et \u00ab d \u00bb. Autrement dit, on fait la multiplication de \u00ab a \u00bb par \u00ab c \u00bb puis par \u00ab d \u00bb et ensuite de \u00ab b \u00bb par \u00ab c \u00bb puis  par \u00ab d \u00bb.&nbsp;<\/p>\n\n\n\n<p>Ce qui nous am\u00e8ne \u00e0 : <strong>(a + b) (c + d) = ac + ad + bc + bd<\/strong>.<br>D\u2019ailleurs, c&#8217;est pareil avec la soustraction : (a + b) (c &#8211; d) = a x c + a x (-d) + b x c + b x (-d) = ac &#8211; ad + bc &#8211; bd.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udea8\u00a0 Petit rappel sur les nombres n\u00e9gatifs<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Regarde bien ce d\u00e9veloppement !\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">(a \u2013 b) (c \u2013 d)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">= a x c + a x (-d) + (-b) x c + (-b) x (-d)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">= ac + (-ad) + (-bc) + bd\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">= ac \u2013 ad \u2013 bc + bd.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">En effet, lorsque tu multiplies un chiffre positif avec un chiffre n\u00e9gatif, le r\u00e9sultat est n\u00e9gatif. Ex : 3 (-4) = -12.\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">Mais, <\/span><b>lorsque tu multiplies deux chiffres n\u00e9gatifs entre eux, cette fois, le r\u00e9sultat est positif<\/b><span style=\"font-weight: 400\">. Ex : (-3) x (-7) = 21.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Tu sais d\u00e9sormais ce qu\u2019est la distributivit\u00e9, ce qui est la base des calculs litt\u00e9raux, mais corsons un peu les choses !<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zdWJqZWN0PU1hdGhzJnNpZ251cD10cnVl\" data-banner=\"2\" data-name=\"CPM2 Maths\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                   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<svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Martin2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Martin<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">23\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Alma2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Alma<\/p>                          <p class=\"push__teachers-school\">ENS Paris-Saclay<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Cle\u0301mence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Ton premier <span style=\"color: #4cc483;\">cours particulier<\/span> de maths est <span style=\"color: #4cc483;\">offert<\/span> ! <span role=\"image\" aria-label=\"\ud83c\udf81\">\ud83c\udf81<\/span><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Tous nos profs sont pass\u00e9s par les meilleures \u00e9coles de France !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        J\u2019EN PROFITE !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">&nbsp;Les calculs litt\u00e9raux : encore plus loin \ud83d\ude80 !<\/h2>\n\n\n\n<p>Apr\u00e8s avoir vu les bases, on va aller un peu plus loin et voir <strong>comment les lettres peuvent \u00eatre utilis\u00e9es dans tes cours de math\u00e9matiques<\/strong>. <\/p>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p>Apprends diff\u00e9remment et regarde notre article sur <a href=\"https:\/\/sherpas.com\/blog\/film-maths\/\">7 films qui vont te faire aimer les maths \ud83c\udfa5 !\u00a0<\/a><\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\">L\u2019expression litt\u00e9rale \ud83d\udd8b\ufe0f<\/h3>\n\n\n\n<p>Une expression litt\u00e9rale peut s\u2019apparenter \u00e0 : A = 5a + 6b \u2013 4 par exemple.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 Pour info<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Une lettre est aussi appel\u00e9e \u00ab variable \u00bb dans une expression litt\u00e9rale.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Il est primordial de <strong>mettre en ordre une expression<\/strong>, au risque de tout fausser \u274c.<\/p>\n\n\n\n<p>Pour cela, <strong>il faut ordonner de fa\u00e7on d\u00e9croissante les exposants des variables<\/strong>.<\/p>\n\n\n\n<p>Voici l\u2019expression litt\u00e9rale B = 15 + 7x\u00b2 \u2013 3x + x\u00b3 &nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>Pour rendre que cette expression soit plus lisible et coh\u00e9rente, il faut l\u2019\u00e9crire sous cette forme : B = x\u00b3 + 7x\u00b2 \u2013 3x + 15. \u2705<\/p>\n\n\n\n<p>D\u2019ailleurs, dans une expression litt\u00e9rale o\u00f9 le signe \u00ab &#8211; \u00bb est plac\u00e9 devant des parenth\u00e8ses<strong>, il faut changer les signes des termes \u00e0 l\u2019int\u00e9rieur de ces parenth\u00e8ses<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Ex : B = (3x\u00b2 + 5x\u00b2 + x\u00b2) &#8211; (7x + 2x &#8211; 6)&nbsp;<\/p>\n\n\n\n<p>B = 3x\u00b2 + 5x\u00b2 + x\u00b2 &#8211; 7x &#8211; 2x + 6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>B = 9x\u00b2 &#8211; 9x + 6<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Les identit\u00e9s remarquables \ud83d\udc40<\/h3>\n\n\n\n<p>Elles permettent d\u2019acc\u00e9l\u00e9rer des calculs, notamment<strong> pour r\u00e9soudre des \u00e9quations du second degr\u00e9<\/strong>\u00a0(x<sup>2<\/sup>). En bref, tu dois simplement les <a href=\"https:\/\/sherpas.com\/blog\/comment-apprendre-par-coeur-rapidement\/\">apprendre par c\u0153ur<\/a> : les 3 identit\u00e9s remarquables que l\u2019on va voir te permettront par la suite de d\u00e9velopper ou factoriser en un seul coup. Finis les longs calculs !<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/chzz1FQgqhytWRWbp3\/giphy.gif\" alt=\"Les mignons qui sont tous content\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">Carr\u00e9 d\u2019une diff\u00e9rence \u2796<\/h4>\n\n\n\n<p>(a-b)\u00b2 = (a-b) (a-b) = a\u00b2 \u2013 ab &#8211; ba + b\u00b2<\/p>\n\n\n\n<p>Donc <strong>(a-b)\u00b2 = a\u00b2 \u2013 2ab + b\u00b2<\/strong><\/p>\n\n\n\n<p>Le carr\u00e9 d\u2019une somme \u2795&nbsp;<\/p>\n\n\n\n<p>(a+b)\u00b2 = (a+b) (a+b) = a\u00b2 + ab + ba + b\u00b2<\/p>\n\n\n\n<p>Ce qui nous donne : <strong>(a+b)\u00b2 = a\u00b2 + 2ab + b\u00b2<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Produit de la somme par la diff\u00e9rence \u2795\u2796<\/h4>\n\n\n\n<p>(a+b)(a-b) = a x a + a x (-b) + b x a + b x (-b) = a\u00b2 \u2013 ab + ab \u2013 b\u00b2<\/p>\n\n\n\n<p>Donc <strong>(a+b)(a-b) = a\u00b2 \u2013 b\u00b2<\/strong><\/p>\n\n\n\n<p>Et voil\u00e0 retiens ces trois r\u00e9sultats et tu feras des merveilles dans ton cours. D\u2019ailleurs si tu souhaites t\u2019am\u00e9liorer, n\u2019h\u00e9site pas \u00e0 prendre <a href=\"https:\/\/sherpas.com\/cours\/maths\/online\">des cours particuliers de maths en ligne<\/a> avec l\u2019un de nos Sherpas !&nbsp;<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zaWdudXA9dHJ1ZQ==\" data-banner=\"2\" data-name=\"Cours part&amp;#8217; global #1 = CPG1\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Fanny2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fanny<\/p>                          <p class=\"push__teachers-school\">Ponts ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Jade2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Jade<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Margot2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Margot<\/p>                          <p class=\"push__teachers-school\">Arts et M\u00e9tiers ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">22\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Antoine2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Antoine<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">18\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Fabien2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fabien<\/p>                          <p class=\"push__teachers-school\">T\u00e9l\u00e9com Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Alma2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Alma<\/p>                          <p class=\"push__teachers-school\">ENS Paris-Saclay<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Olivier2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Olivier<\/p>                          <p class=\"push__teachers-school\">La Sorbonne<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    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            <svg >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">13\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Sophie2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Sophie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Bordeaux<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">12\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Ton premier cours particulier est offert ! <span role=\"img\" aria-label=\"\ud83c\udf81\">\ud83c\udf81<\/span><!-- notionvc: 91b6b7d7-50f2-46f4-ae1f-ecbabe834aad --><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos profs sont pass\u00e9s par les meilleures \u00e9coles et universit\u00e9s.<!-- notionvc: 21bb66b6-b36d-4ce8-8950-173722d75a1e --><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: #ffffff; border-color: ; background-color: \"\n\n                                    >\n                                        J&#8217;EN PROFITE MAINTENANT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\">&nbsp;Les \u00e9quations \ud83d\udff0<\/h3>\n\n\n\n<p>Finissons par un mot qui en effraie beaucoup, surtout au coll\u00e8ge : les \u00e9quations \ud83d\ude31 !&nbsp;<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 D\u00e9finition<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><b>Une \u00e9quation lie des inconnues \u00e0 des valeurs connues<\/b><span style=\"font-weight: 400\">. Et pour le point historique, l\u2019\u00e9tude des \u00e9quations (connue, aujourd&#8217;hui, sous le nom \u00ab alg\u00e8bre \u00bb) a nettement progress\u00e9 gr\u00e2ce aux recherches des math\u00e9maticiens arabo-persans \ud83c\udf0d.<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<h4 class=\"wp-block-heading\">Les \u00e9quations du premier degr\u00e9 \u2668\ufe0f<\/h4>\n\n\n\n<p>Ce sont <strong>les \u00e9quations qui s\u2019\u00e9crivent sous la forme &#8220;ax + b = cx + d&#8221;<\/strong> o\u00f9 a, b, c et d sont des nombres tels que a\u2260b (a est diff\u00e9rent de b). D\u2019ailleurs, une \u00e9quation du premier degr\u00e9 a une unique solution.<\/p>\n\n\n\n<p>Passons \u00e0 un exemple, afin que tu comprennes au mieux. Essayons de r\u00e9soudre 6x &#8211; 7 = 4x + 3.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\u21aa\ufe0f Info<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Pour r\u00e9soudre une \u00e9quation du premier degr\u00e9, on rassemble les variables avec l\u2019exposant \u00ab x \u00bb ensemble, et d\u2019un autre c\u00f4t\u00e9 les variables sans exposant.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><b>Pour faire passer une variable de l\u2019autre c\u00f4t\u00e9 du signe \u00e9gal, il faut inverser son signe<\/b><span style=\"font-weight: 400\">. <\/span><b>\u26d4<\/b><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Dans notre cas, on met \u00ab 4x \u00bb \u00e0 gauche et cela donne :<\/p>\n\n\n\n<p>Premi\u00e8rement, 6x &#8211; 7 &#8211; 4x = 3<\/p>\n\n\n\n<p>Deuxi\u00e8mement, on fait passer le \u00ab -7 \u00bb \u00e0 droite, ce qui nous am\u00e8ne \u00e0 :&nbsp;<\/p>\n\n\n\n<p>6x &#8211; 4x = 3 + 7<\/p>\n\n\n\n<p>Troisi\u00e8mement, on calcule chaque c\u00f4t\u00e9 :&nbsp;<\/p>\n\n\n\n<p>2x = 10<\/p>\n\n\n\n<p>Et pour finir, on divise par deux chaque c\u00f4t\u00e9 de l\u2019\u00e9quation pour arriver \u00e0 une solution o\u00f9 X est \u00e9gal \u00e0 un nombre, ce qui nous donne :&nbsp;<\/p>\n\n\n\n<p>2x\/2 = 10\/2<\/p>\n\n\n\n<p><strong>X = 5<\/strong><\/p>\n\n\n\n<p>On peut m\u00eame v\u00e9rifier notre r\u00e9ponse en reprenant le probl\u00e8me de d\u00e9part :&nbsp;<\/p>\n\n\n\n<p>6 x 5 &#8211; 7 = 4 x 5 + 3<\/p>\n\n\n\n<p>30 &#8211; 7 = 20 + 3<\/p>\n\n\n\n<p>23 = 23<\/p>\n\n\n\n<p>Ce qui est juste ! F\u00e9licitations \u00e0 tous \ud83c\udf89 !<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/6nuiJjOOQBBn2\/giphy.gif\" alt=\"Barney Stinson qui applaudit\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\">Les \u00e9quations du second degr\u00e9 \ud83e\udd75<\/h4>\n\n\n\n<p>Quant aux <strong>\u00e9quations du second degr\u00e9, elles prennent la forme ax\u00b2+bx+c=0 <\/strong>(avec a qui est non nul).&nbsp;La premi\u00e8re \u00e9tape consiste \u00e0 <strong>calculer le discriminant delta \u0394<\/strong>.&nbsp; Pour se faire, il suffit d\u2019appliquer cette formule :<strong> \u0394 = b\u00b2 \u2013 4ac.<\/strong>&nbsp;<\/p>\n\n\n\n<p>Ensuite, selon le r\u00e9sultat, on va pouvoir en d\u00e9duire le nombre de solutions \u00e0 trouver.<\/p>\n\n\n\n<p>\u274c Si \u0394 &lt; 0 : il n\u2019y a aucune solution.&nbsp;<\/p>\n\n\n\n<p>\ud83d\udc4d Ou alors, si \u0394 = 0 : il y a une seule solution qu\u2019on calculera avec<strong> x = -b\/2a<\/strong><\/p>\n\n\n\n<p>\ud83e\udd1eEt dernier cas de figure, si \u0394 &gt; 0 : il y a deux solutions qu\u2019on calculera avec <strong>x1 = (-b+\u221a\u0394)\/(2a) et x2 = (-b &#8211; \u221a\u0394)\/(2a)<\/strong>.<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1Exemple<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p><span style=\"font-weight: 400\">Calculons le discriminant 2&#215;2 \u2212 x \u2212 6 = 0.<\/span><\/p>\n<p><span style=\"font-weight: 400\">On a donc, a = 2, b = -1 et c = -6\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">Ce qui donne, \u0394 = b2 \u2013 4ac = (-1)2 \u2013 4 x 2 x (-6) = 49. Comme \u0394 &gt; 0, l&#8217;\u00e9quation poss\u00e8de deux solutions distinctes :\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">x1 = (-(-1) + \u221a49)) \/ 2 x 2<\/span><\/p>\n<p><span style=\"font-weight: 400\">= (1+7) \/ 4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= 8\/4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= 2\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">x2 = (-(-1) &#8211; \u221a49)) \/ 2 x 2<\/span><\/p>\n<p><span style=\"font-weight: 400\">= (1-7) \/ 4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= -6\/4<\/span><\/p>\n<p><span style=\"font-weight: 400\">= -3\/2<\/span><\/p>\n\n        <\/div>\n              <\/section>\n\n\n\n<p>Voil\u00e0, les deux solutions de cette \u00e9quation du second degr\u00e9 sont : x1 = 2 et x2 = -3\/2.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>On a fait le tour des calculs litt\u00e9raux et de <strong>tous les th\u00e8mes que tu aborderas au cours de ton ann\u00e9e <\/strong>\ud83d\udcda ! Et si tu ne comprends toujours rien \u00e0 tout ce charabia, tu peux <a href=\"https:\/\/sherpas.com\/cours\/maths\">prendre des cours de maths avec les Sherpas<\/a> !<\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;265182&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;5&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;4.6&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Tu as aim\u00e9 cet article ?&quot;,&quot;legend&quot;:&quot;4.6\\\/5 - (5 votes)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Calculs litt\u00e9raux : un monde sans chiffres \ud83d\ude2f !\u00a0&quot;,&quot;width&quot;:&quot;130.9&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 130.9px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            4.6\/5 - (5 votes)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Toi qui pensais que les math\u00e9matiques n&#8217;\u00e9taient que des calculs avec des chiffres et des nombres, d\u00e9sol\u00e9 de (&#8230;)<\/p>\n","protected":false},"author":356,"featured_media":265183,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"category":[803,810],"tag":[77,770,79],"class_list":["post-265182","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-college","tag-fiche-revision","tag-lycee"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/265182","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/356"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=265182"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/265182\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/265183"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=265182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=265182"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=265182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}