Exo 86 :
a. x(x+4) = -4 => x²+4x+4=0 => (x+2)² = 0 => x + 2 = 0 => x = -2
b. (x+1)³ - (x+1)² = 0 => (x+1)²(x+1-1) = 0 => (x+1)² = 0 ou x = 0 => x = -1 ou x = 0
c. 4x²-2x = 6(2x-1) => 4x²-2x-12x+6 = 0 => 4x²-14x+6=0 (D = 196-96 = 100, donc
racine(D) = 10, c'est à dire 2 solutions) => x = 3 ou x =1/2
d. (x+2)²-3x-6 = 0 => x²+4x+4-3x-6 = 0 => x²+x-2 = 0 => (D = 1+8 = 9, donc r(D) = 3)
=> x = 1 ou x = -2
Exo 93 :
1. -2(x-2)² = -2(x²-4x+4) = -2x²+8x-8 = g(x)
2. g(0) = -2(0-2)² = -2 * 4 = -8 (Le point d'intersection avec l'axe des ordonnées est de
cordonnées (0,-8)
3. Les points sont les solutions de l'équation g(x) = 0
=> g(x) = 0 => -2(x-2)² = 0 => x-2 = 0 => x = 2
Le point d'intersection avec l'axe des abscisses est de cordonnées (2,0)
4. g(x) = -8 => -2x²+8x-8 = -8 => -2x²+8x = 0 => x(-2x+8) = 0
=> x = 0 ou x = 4
Exo 105 :
a. (x-1)/4x = 2 => x-1 = 8x => 7x = -1 => x = -1/7
b. (x²+2x+1)/(x-1) = 0 => x²+2x+1 = 0 => (D = 4-4 = 0 => une seule solution)
=> x = -1
c. ((2/3)x-2)/(2x-6) = 0 => (2/3)x-2 = 0 => (2/3)x = 2 => (1/3)x = 1 => x = 3
Ca a pris du temps :p Mais bon courage ^_^
