Решите уравнение x^2-6x+√х-4=√x-4 - 5

ОДЗ:

x - 4 ≥ 0

x ≥ 4

x² - 6x + √ (x - 4) = √ (x - 4) - 5

x² - 6x + 5 + √ (x - 4) - √ (x - 4) = 0

x² - 6x + 5 = 0

x² - 5x - x + 5 = 0

x (x - 5) - (x - 5) = 0

(x - 1) (x - 5) = 0

x = 1 - не уд. ОДЗ; x = 5.

Ответ: x = 5.