Question

Решить
lg(12x-x²-19)=2lg(x-1)

Answer 1

ОДЗ
6 - √17 < x < 6 + √17  -->
1,87 <x < 10,12

lg(12x - x² - 19) = 2lg(x - 1)
lg(12x - x² - 19) = lg(x - 1)^2
12x - x² - 19 = (x - 1)^2
- x^2 + 12x - 19 = x^2 - 2x + 1
- x^2 + 12x - 19 - x^2 + 2x - 1 = 0 
- 2x^2 + 14x - 20 = 0   /:(-2)
x^2 - 7x + 10 = 0 
D = 49 - 40 = 9
x1 = (7 + 3)/2 = 5 ∈ ОДЗ
x2 = (7 - 3 )/2 = 2 ∈ ОДЗ


Ответ
2; 5