§ 5: 5.6

5.6 Знайдіть множину розв’язків нерівності:

2) (x2 + 7x)(x2 – 7x + 6) < 0,x(x + 7)(x – 1)(x – 6) < 0,x ∈ (–7; 0) ∪ (1; 6);3) x2- x-12x2- 36 ≤ 0, x+3(x-4)x-6(x+6) ≤ 0,x ∈ (–6; –3] ∪ [4; 6);

4) 3x2+ 2x-14x2- x-3 ≥ 0.

a) 3x² + 2x – 1 = 0, D = 4 + 12 = 16, x₁ = -2+46 = 26 = 13,

x₂ = -2-46 = –1;

б) 4x² – x – 4 = 0, D = 1 + 48 = 49, x₁ = 1+78 = 1, x₂ = 1-78 = –68 = –14.

3х- 13(х+1)4х+ 34(х-1) ≥ 0,х ∈ (–∞; –1] ∪ (–34; 13] ∪ (1; +∞).