Réponse :
Explications étape par étape
Bonsoir
Developper :
A = (3 - x)^2 - (3 - x)(5 + x) + 5(9 - x^2)
A = 9 - 6x + x^2 - (15 + 3x - 5x - x^2) + 45 - 5x^2
A = 9 - 6x + x^2 - 15 + 2x + x^2 + 45 - 5x^2
A = -3x^2 - 4x + 39
Factoriser :
A = (3 - x)^2 - (3 - x)(5 + x) + 5(9 - x^2)
A = (3 - x)^2 - (3 - x)(5 + x) + 5(3 - x)(3 + x)
A = (3 - x)(3 - x - 5 - x + 5(3 + x))
A = (3 - x)(-2 - 2x + 15 + 5x)
A = (3 - x)(3x + 13)
Résoudre :
A = 0
A = (3 - x)(3x + 13) = 0
3 - x = 0 ou 3x + 13 = 0
x = 3 ou 3x = -13
x = 3 ou x = -13/3
A = 39
A = -3x^2 - 4x + 39 = 39
-3x^2 - 4x = 39 - 39
-x(3x + 4) = 0
-x = 0 ou 3x + 4 = 0
x = 0 ou 3x = -4
x = 0 ou x = -4/3
