Решите неравенство 12/(x-1)^2-2>=0

Question

Решите неравенство
12/(x-1)^2-2>=0

Answer 1

12/(x-1)²-2≥0   ОДЗ:  х-1≠0  х≠1
(12-2*(x-1)²)/(x-1)²≥0
(12-2x²+4x-2)/(x-1)²≥0
-2*(x²-2x-5)/(x-1)²≥0   I÷(-2)
(x²-2x-5)/(x-1)²≤0
(x-1-2√6)(x-1+2√6)/(x-1)²≤0
-∞______+______1-2√6______-______1+2√6_______+______+∞
Ответ:  x∈[1-2√6;1+2√6].