Bonjour
On considère l'expression
A = (x – 3)²+ (x − 3)(1 – 2x)
1) Développer et réduire A.
A = (x – 3)²+ (x − 3)(1 – 2x)
A = x² - 6x + 9 + x - 2x² - 3 + 6x
A = x² - 2x² - 6x + 6x + x + 9 - 3
A = - x² + x + 6
2) Factoriser A.
A = (x – 3)²+ (x − 3)(1 – 2x)
A = (x - 3) (x - 3 + 1 - 2x)
A = (x - 3) (- x - 2)
3) Calculer A pour x = -2
A = - x² + x + 6
A = (- 2)² - 2 + 6
A = 4 + 4
A = 8
4) Résoudre (x – 3)(-x - 2) = 0
(x - 3) = 0 ou - x - 2 = 0
x = 3 - x = 2
x = - 2.
