Bonjour,
1) 2x²-3 ≤ 6
2x²- 9 ≤ 0 je pose donc a = 2; b = 0; c = -9
delta = b² - 4*a*c = 0 - 4*2*(-9) = 72
2 solutions pour 2x²- 9 = 0 -->
--> x1 = [tex]\frac{-b-\sqrt{delta} }{2a} =\frac{-\sqrt{72} }{4} = \frac{-6*\sqrt{2} }{4} = \frac{-3\sqrt{2} }{2}[/tex]
--->x2 = [tex]\frac{-b+\sqrt{delta} }{2a} =\frac{\sqrt{72} }{4} = \frac{6*\sqrt{2} }{4} = \frac{3\sqrt{2} }{2}[/tex]
Tbleau1 de signe
S = [x1 ; x2]
2)
-5x²+10 > x²-8
-6x² + 18 > 0 je pose a = -6; b=0 ; c = 18
delta = b² - 4*a*c = 0 -4 * (-6) * 18 = 432
2 solutions pour -4x² + 18 = 0
x1 = [tex]\frac{-b+\sqrt{delta} }{2a} =\frac{\sqrt{432} }{-12} = \frac{12*\sqrt{3} }{-12} = -\sqrt{3}[/tex]
x2 = [tex]\frac{-b-\sqrt{delta} }{2a} =\frac{-\sqrt{432} }{-12} = \frac{12*\sqrt{3} }{12} = \sqrt{3}[/tex]
Tableau2 de signe:
S = ] x1 ; x2 [
Bonne journée :)
