Решите неравенство: |x^2 - 8| < либо = 2x

Question

Решите неравенство:
|x^2 - 8| < либо = 2x

Answer 1

|x² - 8| ≤ 2x,
2x≥0, x≥0;
x²-8=0, (x-√8)(x+√8)=0,
x+2√2=0, x=-2√2,
x-2√2=0, x=2√2;

0≤x≤2√2, x²-8≤0,
-(x²-8)≤2x, x²-8≥-2x, x²+2x-8≥0,
x²+2x-8=0, D/4=1+8=9, x₁=-1-3=-4, x₂=-1+3=2,
x≤-4, x≥2;
2≤x≤2√2;

x≥2√2, x²-8≥0,
x²-8≤2x, x²-2x-8≤0,
x²-2x-8=0, D/4=1+8=9, x₁=1-3=-2, x₂=1+3=4,
-2≤x≤4;
2√2≤x≤4;

2≤x≤4, x∈(2;4).