Question

$5 {}^{2x - 9} < 5 {}^{x {}^{2} - 12 }$
решить неравенство​
Помогите если не сложно

Answer 1

$\displaystyle 5^{2x-9}<5^{x^2-12}\\\\5>1\\\\2x-9<x^2-12\\\\x^2-2x+9-12>0\\\\x^2-2x-3>0\\\\x^2-2x-3=0\\\\D=4+12=16\\\\x_{1.2}=\frac{2 \pm 4}{2}\\\\x_1=3; x_2=-1$

_+___ -1___-__ 3___+___

$x \in (-oo;-1) (3;+oo)$