Question

Решите неравенство!!!!!!!!
|x+7|<|x^2-3x+2|

Answer 1

$|x+7|<|x^2-3x+2|\\(x+7)^2<(x^2-3x+2)^2\\(x^2-3x+2)^2-(x+7)^2>0\\(x^2-3x+2-x-7)(x^2-3x+2+x+7)>0\\(x^2-4x-5)(x^2-2x+9)>0 |:(x^2-2x+9)>0\\x^2-4x-5>0\\x^2-4x+4-9>0\\(x-2)^2-3^2>0\\(x-2-3)(x-2+3)>0\\(x-5)(x+1)>0\\x\in (-\infty; -1) \cup(5; +\infty)\\Answer: x\in (-\infty; -1) \cup(5; +\infty)$