Verified answer

Bonjour

Soit C = (6x – 7)² - (2x – 3)²

1) Développer, réduire et ordonner C.

C = 36x^2 - 84x + 49 - (4x^2 - 12x + 9)

C = 36x^2 - 84x + 49 - 4x^2 + 12x - 9

C = 32x^2 - 72x + 40

2) Factoriser C.

C = (6x - 7 - 2x + 3)(6x - 7 + 2x - 3)

C = (4x - 4)(8x - 10)

C = 4(x - 1) * 2(4x - 5)

C = 8(x - 1)(4x - 5)

3) Résoudre l’équation (4x – 4)(8x – 10) = 0

x - 1 = 0 ou 4x - 5 = 0

x = 1 ou 4x = 5

x = 1 ou x = 5/4