Найдите все корни уравнения (х²-1)²+(х-1)=0

(х² - 1)² + (х - 1) = 0

((x - 1)(x + 1))² + (x - 1) = 0

(x - 1)*((x - 1) * (x + 1)² + 1) = 0

x - 1 = 0 (x - 1) * (x + 1)² + 1 = 0

x = 1 (x - 1) * (x² + 2x + 1) + 1 = 0

x³ + 2x² + x - x² - 2x - 1 + 1 = 0

x³ + x² - x = 0

x(x² + x - 1) = 0

x = 0 x² + x - 1 = 0

D = 1² + 4 * 1 * 1 = 5

x = (-1 - √5)/2

x = (-1 + √5)/2

Ответ: $x = 0;\\ x=1; \\ x=\frac{-1-\sqrt{5} }{2} ;\\ \\ x=\frac{-1+\sqrt{5} }{2}$

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