Замена переменной:
t=x²
t²=x⁴
t²-3t+2≤0
t²-3t+2=0
D=(-3)²-4*2=9-8=1
t₁=(3-1)/2=1
t₂=(3+1)/2=2
+ - +
----------- 1 ------------- 2 -------------
\\\\\\\\\\\\\\\\\
t∈[1; 2]
1≤t≤2
1≤x²≤2
{x²≥1
{x²≤2
x²≥1
x²-1²≥0
(x-1)(x+1)≥0
x=1 x= -1
+ - +
--------- -1 ------------ 1 ------------
\\\\\\\\\\\\\ \\\\\\\\\\\\\\\
x∈(-∞; -1]U[1; +∞)
x²≤2
x²-(√2)²≤0
(x²-√2)(x²+√2)≤0
x=√2 x= -√2
+ - +
----------- -√2 ---------- √2 -----------
\\\\\\\\\\\\\\
x∈[-√2; √2]
{x∈(-∞; -1]U[1; +∞)
{x∈[-√2; √2]
⇒ x∈[-√2; -1]U[1; √2]
Ответ: [-√2; -1]U[1; √2].