Réponse:
Bonsoir
Explications étape par étape:
(x² - 3x - 5)² - 3(x² - 3x - 5) - 5
x⁴ + 9x² - 25 - 6x³ - 10x² + 30x - 3x² + 9x + 15 - 5 =x
x⁴ - 4x² - 35 - 6x³ + 39x = x
x⁴ - 4x² + 35 - 6x³ + 39x - x = 0
x⁴ - 4x² + 35 - 6x³ + 38x = 0
x⁴ - 6x³ - 4x² + 38x + 35 = 0
x⁴ + x³ - 7x³ - 7x² + 3x² + 3x + 35x + 35 = 0
x³(x + 1) - 7x²(x + 1) + 3(x + 1) + 35(x + 1) = 0
(x + 1)(x³- 7x² + 3x + 35) = 0
( x + 1)(x³ - 5x² - 2x² + 10x - 7x + 35) = 0
(x + 1)(x²(x - 5) - 2x(x - 5) - 7(x - 5) = 0
(x + 1)(x - 5)(x² - 2x - 7) = 0
• x + 1 = 0
• x - 5 = 0
• x² - 2x - 7 = 0
• x = -1
• x = 5
• x = 1 + 2√2
• x = 1 - 2√2
