Вправи: 1027

1027. Розв’яжіть рівняння:

1) 5(х – 2) = (Зх + 2)(х – 2); 5х – 10 = Зх² – 6х + 2х – 4;

Зх² – 4х – 4 – 5х + 10 = 0; Зх² – 9х + 6 = 0; х² – Зх + 2 = 0;

D = (–З)2 – 4 • 2 = 1; х1 = 3+12 = 2; х₂ = 3-12 = 1.

2) 15x² – 2x – 7 = 0; x² – 10x – 35 = 0; D=(–10)² – 4 • (–35) = 240;

D = 415; x_1,2 = 10 ±4152 = 2(5 ±215)2 = 5±215.

3) x² + 2x – 12 = 0; D = (2)² – 4 • (–12) = 50; D = 52;

x₁ = -2+ 522 = 422 = 22; x₂ = -2- 522 = -622 = –32.

4) 3x² – 2x – 3 = 0; D = (–2)² – 4 • 3 • (–3) = 4 + 12 = 16;

x₁ = 2+423 = 623 = 33 = 3; x₂ = 2-423 = –223 = –13 = –33.

Відповідь: 1) 1; 2; 2) 5±215; 3) 22; –32; 4) 3; –33.