Question

Lg (x-1) +lg (x- 1) = lg8 +lg (x-2)

Answer 1

Решение
Lg (x-1) +lg (x- 1) = lg8 +lg (x-2)
ОДЗ: x - 1 > 0, x > 1
x - 2 > 0, x > 2
x∈(2 ; + ∞)
Lg (x-1)*(x- 1) = lg8 *(x-2)
(x - 1)² = 8x - 16
x² - 2x + 1 - 8x + 16 = 0
x² - 10x + 17 = 0
D = 100 - 4*1*17 = 32
x = (10 - 4√2)/2
x = 5 - 2√2 не удовлетворяет ОДЗ x∈(2 ; + ∞)
x = (10 + 4√2)/2
x = 5 + 2√2
Ответ:  x = 5 + 2√2