Bonjour
Résoudre les équations suivantes :(
(x²– 9)(x + 1) + (x + 3)(x²- 1) = 0
(x^2 - 3^2)(x + 1) + (x + 3)(x^2 - 1^2) = 0
Du type a^2 - b^2 = (a - b)(a + b)
(x - 3)(x + 3)(x + 1) + (x + 3)(x - 1)(x + 1) = 0
(x + 3)(x + 1)(x - 3 + x - 1) = 0
(x + 3)(x + 1)(2x - 4) = 0
(x + 3)(x + 1) * 2(x - 2) = 0
2(x + 3)(x + 1)(x - 2) = 0
Produit de facteur nul :
x + 3 = 0 ou x + 1 = 0 ou x - 2 = 0
x = -3 ou x = -1 ou x = 2
(x + 1)(6x - 2) - (1 + 2x)(-3x + 1) = 0
(x + 1) * 2(3x - 1) - (1 + 2x)(-3x + 1) = 0
2(x + 1)(3x - 1) + (3x - 1)(1 + 2x) = 0
(3x - 1)[2(x + 1) + 1 + 2x] = 0
(3x - 1)(2x + 2 + 1 + 2x) = 0
(3x - 1)(4x + 3) = 0
3x - 1 = 0 ou 4x + 3 = 0
3x = 1 ou 4x = -3
x = 1/3 ou x = -3/4
x² - 5/x+5 = 0
x^2 - 5)/(x + 5) = 0
(x - V5)(x + V5)/(x + 5) = 0
avec x + 5 # 0
x # -5
Et x - V5 = 0 ou x + V5 = 0
x = V5 ou x = -V5
x²(2x + 1) = 4(2x + 1)
x^2(2x + 1) - 4(2x + 1) = 0
(2x + 1)(x^2 - 4) = 0
(2x + 1)(x - 2)(x + 2) = 0
2x + 1 = 0 ou x - 2 = 0 ou x + 2 = 0
2x = -1 ou x = 2 ou x = -2
x = -1/2 ou x = 2 ou x = -2