§ 44: 44.12 (1-4)

44.12 Розв’яжіть нерівність:

1) (x² – 6x)(x² + 5x – 6) < 0;

x(x – 6)(x + 6)(x – 1) < 0;

x ∈ (–6; 0) ∪ (1; 6).

2) (x² – 4x + 3)(x² + 3x + 2) ≥ 0

x₁ = 3; x₁ = –2;

x₂ = 1; x₂ = –1.

(x – 3)(x – 1)(x + 2)(x + 1) ≥ 0;

x ∈ (–∞; –2] ∪ [–1; 1] ∪ [3; ∞).

3) 4x³ – 25x < 0;

x(4x² – 25) < 0;

x(2x – 5)(2x + 5)< 0;

x = 0; x = 2,5; x = –2,5;

x ∈ (–∞; –2,5) ∪ (0; 2,5).

4) x3- 16xx2- x-30 < 0;

xx-4(x+4)x-6(x+5) < 0;

x ∈ (–∞; –5) ∪ (–4; 0) ∪ (4; 6).

5) (x – 1)(x + 3)²(x – 2) < 0;

x ∈ (1; 2).

6) (2x + 1)²(x² – 4x + 3) > 0;

(2x + 1)²(x – 3)(x – 1)> 0;

x ∈ (–∞; –12) ∪ (–12; 1) ∪ (3; ∞).

7) (2x + 1)²(x 0 1)(x – 2) ≥ 0;

x ∈ (–∞; 1] ∪ [2; +8).

8) (x – 5)(x + 4)(x2 + 6x + 9) ≥ 0;

(x – 5) (x + 4)(x + 3)² ≥ 0;

x ∈ (–∞; –4) ∪ {–3} ∪ [4; ∞)