Задача 50959 ...

sova

2020-05-20 12:08:46

ОДЗ:
{x^2>0 ⇒ [red]x ≠ 0[/red]
{|x| ≠ 1 ⇒ [red]x ≠ ± 1[/red]


log_(|x|)x^2=log_(|x|)(|x|)^2=2log_(|x|)(|x|)=2

log^2_(|x|)x^2=2^2=4


{4*(2^(x))^2-17*2^(x)+4 ≤ 0 ⇒ D=225; (1/4) ≤ 2^(x) ≤ 4
{4+log_(2)x^2 ≤ 8 ⇒ (log_(2)x-2)*(log_(2)x+2) ≤ 0 ⇒ -2 ≤ log_(2)x ≤ 2


{2^(-2) ≤ 2^(x) ≤ 2^2 ⇒ (-2) ≤ x ≤ 2
{log_(2)(1/4) ≤ log_(2)x ≤ log_(2)4 ⇒ (1/4) ≤ x ≤ 4


(1/4) ≤ х ≤ 2

C учетом ОДЗ

О т в е т. [1/4;1) U (1; 2]