Відповіді §.13 - §.14 » §.13 (7.1-3)

Розв’яжіть систему нерівностей: 1. x2 ≤ 4. x2 + 2x – 8 ≤ 0. 2. x2 ≥ 25. x2 – 6x + 5 ≤ 0. x2 ≤ 4. x2 – 4 = 0. x = ± 2. x2 + 2x – 8 ≤ 0. x2 + 2x – 8 = 0. x1 = –4 x2 = 2. x2 ≥ 25. x2 – 25 = 0. x = ±5. x2 – 6x + 5 ≤ 0. x2 – 6x + 5 = 0. x1 = x x2 = 5. x ∈ [–2; 2] x = 5 3. 2x2 – 5x + 2 > 0, x2 – x – 2 ≤ 0. 2x2 – 5x + 2 > 0. 2x2 – 5x + 2 = 0. D = 25 – 4 • 2 • 2 = 9. x1 = (5+3)/4 = 2. x2 = (5-3)/4 = 1/2 x2 – x – 2 ≤ 0. x2 – x – 2 = 0. x1 = 2. x2 = –1. x ∈ [–1; 1/2).