Bonjour,
Résoudre les équations produit nul suivantes en factorisant grâce aux identités remarquables.
a) (5 x−4)²−36=0
(5x - 4 - 6) (5x - 4 + 6) = 0
(5x - 10) (5x + 2) = 0
5x - 10 = 0 ou 5x + 2 = 0
5x = 10 5x = - 2
x = 10/5 = 2 x = - 2/5
b) x ²−6 x+9=0
(x - 3)² = 0
x - 3 = 0
x = 3
c) x ²−49=0
(x - 7) (x + 7) = 0
x - 7 = 0 ou x + 7 = 0
x = 7 x = - 7
d) 9 x ²+24 x+16=0
(3x + 4)² = 0
3x + 4 = 0
3x = - 4
x = - 4/3
e) 36 x ²−144=0
(6x - 12) (6x + 12) = 0
6x - 12 = 0 ou 6x + 12 = 0
6x = 12 6x = - 12
x = 12/6 = 2 x = - 12/6 = - 2
f) (4 x−3)²=81
(4x - 3)² - 81 = 0
(4x - 3 - 9) (4x - 3 + 9) = 0
(4x - 12) (4x + 6) = 0
4x + 12 = 0 ou 4x + 6 = 0
4x = - 12 4x = - 6
x = - 12/4 = - 3 x = - 6/4 = - 3/2
g) (3 x−1)²=1
(3x - 1 - 1) (3x) = 0
3x (3x - 2) = 0
3x = 0 ou 3x - 2 = 0
x = 0 3x = 2
x = 2/3
h) 4 x ²=9
4x² - 9 = 0
(2x - 3) (2x + 3) = 0
2x - 3 = 0 ou 2x + 3 = 0
2x = 3 2x = - 3
x = 3/2 x = - 3/2
