Відповіді на вправи: 476

1) 3x² + 9 > 2x² + 6x;

3x² – 2x² – 6x + 9 > 0;

x² – 6x + 9 > 0;

x² – 6x + 9 = 0;

(x – 3)² = 0;

x – 3 = 0; x = 3.

x ∈ (–∞; 3) ∪ (3; +∞).

2) 4x ≤ –x² + 5;

x² + 4x – 5 ≤ 0;

x² + 4x – 5 = 0;

x₁ = –5, x₂ = 1.

x ∈ [–5; 1].

3) 6x² ≥ 15x – 6;

6x² – 15x + 6 ≥ 0;

D = (–15)² – 4 • 6 • 6 = 81 = 9²;

x₁ = $\frac{15-9}{12}$ = $\frac{6}{12}$ = 0,5;

x₂ = $\frac{15+9}{12}$ = $\frac{24}{12}$ = 2;

x ∈ (–∞; 0,5) ∪ [2; +∞).

4) 2x² > –3x² – 3x + 2;

2x² + 3x² + 3x – 2 > 0;

5x² + 3x – 2 > 0;

D = 9 – 4 • 5 • (–2) = 49 = 7²;

x₁ = $\frac{-3-7}{10}$ = $\frac{-10}{10}$ = –1;

x₂ = $\frac{-3+7}{10}$ = $\frac{4}{10}$ = 0,4;

x ∈ (–∞; –1) ∪ (0,4; +∞)