Réponse :
Explications étape par étape
Bonsoir
Factoriser :
f(x) = (2x - 6)(-12x + 20) + 4(x - 3)(10x - 12)
f(x) = 2(x - 3) * 4(-3x + 5) + 4(x - 3) * 2(5x - 6)
f(x) = 8(x - 3)(-3x + 5 + 5x - 6)
f(x) = 8(x - 3)(2x - 1)
Developper :
f(x) = 8(2x^2 - x - 6x + 3)
f(x) = 8(2x^2 - 7x + 3)
f(x) = 16x^2 - 56x + 24
f(x) = 0 ; f(x) = 24 ; f(x) = 11
8(x - 3)(2x - 1) = 0
x - 3 = 0 ou 2x - 1 = 0
x = 3 ou 2x = 1
x = 3 ou x = 1/2
16x^2 - 56x + 24 = 24
16x^2 - 56x = 24 - 24
8x(2x - 7) = 0
8x = 0 ou 2x - 7 = 0
x = 0 ou 2x = 7
x = 0 ou x = 7/2
16x^2 - 56x + 24 = 11
16x^2 - 56x + 24 - 11 = 0
16x^2 - 56x + 13 = 0
(4x)^2 - 2 * 4x * 7 + 7^2 - 7^2 + 13 = 0
(4x - 7)^2 - 49 + 13 = 0
(4x - 7)^2 - 36 = 0
(4x - 7)^2 - 6^2 = 0
(4x - 7 - 6)(4x - 7 + 6) = 0
(4x - 13)(4x + 1) = 0
4x - 13 = 0 ou 4x + 1 = 0
4x = 13 ou 4x = -1
x = 13/4 ou x = -1/4
