Question

Решите уравнение x^2-6x+√х-4=√x-4 -5

Answer 1

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.