9. Решите уравнение x(x² - 12x +36) = -5(x-6)

Ответ: 6, -1, -5

Решение:

x(x² - 12x + 36) = -5(x - 6)

x(x - 6)² = -5(x - 6)

x(x - 6)² + 5(x - 6) = 0

(x - 6)(x(x - 6) + 5) = 0

(x - 6)(x² - 6x + 5) = 0

Корни: x₁ = 6

x² - 6x + 5 = 0

D = (-6)² - 4 \cdot 1 \cdot 5 = 36 - 20 = 16

x₂ = (6 + \(\sqrt{16}\)) / 2 = (6 + 4) / 2 = 10 / 2 = 5

x₃ = (6 - \(\sqrt{16}\)) / 2 = (6 - 4) / 2 = 2 / 2 = 1

Корни: x₁ = 6, x₂ = 5, x₃ = 1

Ответ: 1, 5, 6