bonsoir, pouver-vous m'aider pour l'ex 1.Merci de votre aide.... Pergunta de ideia dehugo12

January 2021 1 162 Report

bonsoir, pouver-vous m'aider pour l'ex 1.Merci de votre aide

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scoladan

Verified answer

Bonjour,

a) A(x) = (2x + 3)² - (2x + 6)²

= [(2x + 3) - (2x + 6)][(2x + 3) + (2x + 6)]

= -3(4x + 9)

b) A(x) < 0

⇔ -3(4x + 9) < 0

⇔ 4x + 9 > 0

⇔ 4x > -9

⇔ x > -9/4

c) (x + 2)(6x - 1) < (x + 2)(x - 3)

⇔ (x + 2)(6x - 1) - (x + 2) (x - 3) < 0

⇔ (x + 2)[(6x - 1) - (x - 3)] < 0

⇔ (x + 2)(6x - 1 - x + 3) < 0

⇔ (x + 2)(5x + 2) < 0

Tableau de signes

x -∞ -2 -2/5 +∞
(x + 2) -    0 +    +
(5x + 2) - -    0 +
Produit +    0 -    0 +

Donc l'ensemble des solutions est : ]-2 ; -2/5[

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