{"id":268372,"date":"2024-06-17T09:00:00","date_gmt":"2024-06-17T07:00:00","guid":{"rendered":"https:\/\/sherpas.com\/blog\/parents\/?p=268372"},"modified":"2024-06-07T13:24:24","modified_gmt":"2024-06-07T11:24:24","slug":"equations-inequations","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/parents\/a\/equations-inequations\/","title":{"rendered":"D\u00e9mystifier les \u00e9quations et les in\u00e9quations \ud83d\udff0"},"content":{"rendered":"\n

Votre ado vous parle des \u00e9quations et des in\u00e9quations et cela vous rappelle de mauvais souvenirs de math\u00e9matiques.<\/strong> \ud83d\udcad<\/p>\n\n\n\n

Pas d\u2019inqui\u00e9tude ! Nous allons tout vous expliquer pour que vous soyez de vrais pros \u00e0 la table des devoirs ! \ud83e\uddb8<\/p>\n\n\n

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\u00c0 lire aussi<\/p>\n

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D\u00e9couvrez comment r\u00e9concilier votre ado en maths<\/a> avec notre article !<\/p>\n\n <\/div>\n <\/section>\n\n\n

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\n \n PRENDRE UN COURS D’ESSAI OFFERT\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n\n\n

Comprendre les \u00e9quations <\/h2>\n\n\n\n

D\u00e9finition<\/h3>\n\n\n\n

R\u00e9soudre une \u00e9quation, c\u2019est d\u00e9terminer toutes les valeurs de l\u2019inconnue<\/strong> (ou des inconnues) pour lesquelles l\u2019\u00e9galit\u00e9 est v\u00e9rifi\u00e9e<\/strong>. Chacune de ces valeurs est appel\u00e9e solution de l\u2019\u00e9quation. \u2705<\/strong><\/p>\n\n\n

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\u00c9quation du premier degr\u00e9\u2699\ufe0f<\/p>\n<\/div>\n

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On appelle \u00e9quation du premier degr\u00e9 \u00e0 une inconnue<\/strong> toute \u00e9quation pouvant se ramener \u00e0 une \u00e9quation du type ax<\/em> = b, o\u00f9 x<\/em> est l\u2019inconnue.<\/p>\n\n <\/div>\n <\/section>\n\n\n\n

Exemples <\/h3>\n\n\n\n

8x <\/em>+ 6 = -5x <\/em>+26<\/p>\n\n\n\n

8x + <\/em>5x <\/em>= 26 – 6<\/p>\n\n\n\n

13x <\/em>= 20<\/p>\n\n\n\n

 x <\/em>= 20 \u2044 13<\/p>\n\n\n\n

La solution de l\u2019\u00e9quation est 20 \u2044 13.<\/p>\n\n\n\n

-3(2x<\/em> – 6) + 12 = 6 – 4 (x<\/em> +1)<\/p>\n\n\n\n

-6x<\/em> + 18 + 12 = -6 – 4x<\/em> – 4<\/p>\n\n\n\n

-6x <\/em>+ 4x<\/em> = -6 -4 – 18 – 12<\/p>\n\n\n\n

-2x = -40<\/p>\n\n\n\n

x<\/em> = -40\u2044-2<\/p>\n\n\n\n

x<\/em> = 20<\/p>\n\n\n\n

La solution de l\u2019\u00e9quation est 20.<\/p>\n\n\n

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\u00c9quation du second degr\u00e9\u2699\ufe0f<\/p>\n<\/div>\n

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Une \u00e9quation du second degr\u00e9 est une \u00e9quation de la forme ax\u00b2 + bx +c = 0.\u00a0<\/strong><\/p>\n\n <\/div>\n <\/section>\n\n\n\n

Exemple : <\/h3>\n\n\n\n

Pour cet exemple, prenons a = 1<\/strong>, b = -3<\/strong>, et c = 2<\/strong>. Donc, notre \u00e9quation devient x\u00b2\u22123x+2=0<\/p>\n\n\n\n

Pour r\u00e9soudre cette \u00e9quation, nous allons utiliser les formule suivante :  x1<\/em> = [-b +\u221a(b\u00b2 – 4a)] \u2044[2a] et <\/p>\n\n\n\n

x2<\/em> = [-b -\u221a(b\u00b2 – 4a)] \u2044[2a].<\/p>\n\n\n\n

x1<\/em> = [3 +\u221a((-3)\u00b2 – 4 X 1 X2)] \u2044 [2 X 1]  et x2<\/em> = [3 – \u221a((-3)\u00b2 – 4 X 1 X2)] \u2044 [2 X 1]    <\/p>\n\n\n\n

x1 = [3 +\u221a(9 – 8)] \u2044 2 et x2 = [3 -\u221a(9 – 8)] \u2044 2<\/p>\n\n\n\n

Donc les solutions sont x1<\/em> = [3 +1]\u20442 = 2 et x2<\/em> = [3 -1]\u20442 = 1.<\/p>\n\n\n

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\u00c9quation produit\u2699\ufe0f<\/p>\n<\/div>\n

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Une \u00e9quation produit est de la forme f(x) X g(x) = a<\/strong><\/p>\n\n <\/div>\n <\/section>\n\n\n\n

<\/p>\n\n\n\n

Exemples <\/h3>\n\n\n\n

Soit l’\u00e9quation  (3\ud835\udc65\u22125)(\ud835\udc65+2)=4<\/p>\n\n\n\n

(3\ud835\udc65\u22125)(\ud835\udc65+2)=4<\/p>\n\n\n\n

On d\u00e9veloppe l’\u00e9quation.<\/p>\n\n\n\n

3x\u00b2 +x -10 = 4<\/p>\n\n\n\n

3x\u00b2 +x – 14 = 0<\/p>\n\n\n\n

Ensuite, on utilise la formule suivante : x1<\/em> = [-b +\u221a(b\u00b2 – 4a)] \u2044[2a] et x2<\/em> = [-b -\u221a(b\u00b2 – 4a)] \u2044[2a].<\/p>\n\n\n\n

x1<\/em> = [-1 +\u221a(1\u00b2 – 4 X 3 X (-14))] \u2044[2 X 3]      x2<\/em> = [-1 -\u221a(1\u00b2 – 4 X 3 X (-14))] \u2044[2 X 3]<\/p>\n\n\n\n

x1<\/em> = [-1 +13] \u2044[2 X 3]   = 2   x2<\/em> = [-1 -13] \u2044[2 X 3]   = -73<\/p>\n\n\n\n

C\u2019est-\u00e0-dire x1<\/em> = 2 ou x2<\/em> = -73<\/p>\n\n\n

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\u00c0 lire aussi<\/p>\n

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D\u00e9couvrez comment d\u00e9velopper et factoriser<\/a>\u00a0en math\u00e9matiques !<\/p>\n\n <\/div>\n <\/section>\n\n\n

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\u00c9quation quotient \u2699\ufe0f<\/p>\n<\/div>\n

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Une \u00e9quation quotient est de la forme f(x) \u2044g(x) = a<\/p>\n\n <\/div>\n <\/section>\n\n\n\n

Exemples <\/h3>\n\n\n\n

(x +2) \u2044(3x+4) =4<\/p>\n\n\n\n

x + 2 = 4 (3x + 4)<\/p>\n\n\n\n

x + 2 = 12x +16<\/p>\n\n\n\n

x = 12x + 14<\/p>\n\n\n\n

-11x = 14<\/p>\n\n\n\n

x = -14 \u2044-11<\/p>\n\n\n\n

En passant, si votre ado a des difficult\u00e9s en math\u00e9matiques, prenez-lui des cours de soutien en maths<\/a> pour l\u2019aider \u00e0 remonter sa moyenne !<\/p>\n\n\n

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