Résoudre les inéquations a) 2(x - 3)(5 - 4x) ≤ 0b) - x(3x + 4) > 0Merci.... Pergunta de ideia deYumi0

April 2019 1 110 Report

Résoudre les inéquations
a) 2(x - 3)(5 - 4x) ≤ 0
b) - x(3x + 4) > 0

Merci.

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Commentaires Bonsoir,

Ces inéquations se résolvent par des tableaux de signes.

a) 2(x - 3)(5 - 4x) ≤ 0

racines : x - 3 = 0 ==> x = 3
5 - 4x = 0 ==> -4x = -5 ==> x = (-5)/(-4) = 5/4

$\begin{array}{|c|ccccccc||}x&-\infty&&\dfrac{5}{4}&&3&&+\infty\\ 2(x-3)&&-&-&-&0&+&\\ 5-4x&&+&0&-&-&-&\\ 2(x-3)(5-4x)&&-&0&+&0&-& \\\end{array}\\\\\\S=]-\infty;\dfrac{5}{4}]\ \cup\ [3;+\infty[$

b) - x(3x + 4) > 0

racines : -x = 0 ==> x = 0
3x + 4 = 0 ==> 3x = -4 ==> x = -4/3

$\begin{array}{|c|ccccccc||}x&-\infty&&-\dfrac{4}{3}&&0&&+\infty\\ -x&&+&+&+&0&-&\\ 3x+4&&-&0&+&+&+&\\ -x(3x+4)&&-&0&+&0&-& \\\end{array}\\\\\\S=]-\dfrac{4}{3};0[$

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