Réponses

Meilleure réponse !
2014-01-17T23:15:39+01:00
Bonsoir

(\dfrac{x}{2}-\dfrac{3}{4})x-\dfrac{x-3}{2}\le (\dfrac{x}{4}-\dfrac{2}{3})x-\dfrac{x-6}{4}\\\\(\dfrac{4x-6}{8})x-\dfrac{x-3}{2}\le (\dfrac{3x-8}{12})x-\dfrac{x-6}{4}\\\\(\dfrac{12x-18}{24})x-\dfrac{12x-36}{24}\le \dfrac{6x-16}{24})x-\dfrac{6x-36}{24}\\\\\dfrac{(12x-18)x-(12x-36)}{24}\le \dfrac{(6x-16)x-(6x-36)}{24}\\\\(12x-18)x-(12x-36)\le (6x-16)x-(6x-36)\\\\12x^2-18x-12x+36\le6x^2-16x-6x+36\\\\12x^2-30x+36\le6x^2-22x+36


12x^2-30x+36-6x^2+32x-36\le0\\\\6x^2-8x\le0\\\\2x(3x-4)\le0

Tableau de signes.

Racines : 2x = 0 ==> x = 0
                3x - 4 = 0 ===> 3x = 4 
                                 ===> x = 4/3

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