Bonsoir,
a) 4x² - 9 ≤ 0
(2x)² - 3² ≤ 0
(2x + 3)(2x - 3) ≤ 0
Tableau de signes.
Racines : 2x + 3 = 0 ==> 2x = -3
==> x = -3/2
2x - 3 = 0 ==> 2x = 3
==> x = 3/2
[tex]\begin{array}{|c|ccccccc|}x&-\infty&&-\frac{3}{2}&&\frac{3}{2}&&+\infty \\ 2x+3&&-&0&+&+&+&\\2x-3&&-&-&-&0&+&\\ (2x+3)(2x-3)&&+&0&-&0&+&\\ \end{array}\\\\\\ (2x+3)(2x-3)\le0\Longleftrightarrow x\in\ [-\dfrac{3}{2};\dfrac{3}{2}]\\\\ S=[-\dfrac{3}{2};\dfrac{3}{2}][/tex]
b) (x+3)² - 4 ≥ 0
(x+3)² - 2² ≥ 0
[(x+3) + 2][(x+3) - 2] ≥ 0
(x + 3 + 2)(x + 3 - 2) ≥ 0
(x + 5)(x + 1) ≥ 0
Tableau de signes.
Racines : x + 5 = 0 ==> x = -5
x +1 = 0 ==> x = -1
[tex]\begin{array}{|c|ccccccc|}x&-\infty&&-5&&-1&&+\infty \\ x+5&&-&0&+&+&+&\\x+1&&-&-&-&0&+&\\ (x+5)(x+1)&&+&0&-&0&+&\\ \end{array}\\\\\\(x+5)(x+1)\ge0\Longleftrightarrow x\in]-\infty;-5]\ \cup\ [-1;+\infty[\\\\S=]-\infty;-5]\ \cup\ [-1;+\infty[[/tex]
