Відповіді до вправ § 20 - § 26: 21.13

21.13 Розв’яжіть рівняння:

1) (x + 2)² = 2x + 3; x² + 4x + 4 – 2х – 3 = 0; x² + 2x + 1 = 0;

D = 2² – 4 • 1 • 1 = 0;

х = -22 = –1.

2) 5(x – 2)² = 3х – 6; 5(x² – 4x + 4) – 3х + 6 = 0;

5x² – 20x + 20 – 3х + 6 = 0; 5x² – 23x + 26 = 0;

D = (–23)² – 4 • 5 • 26 = 9; D = 3;

х₁ = 23+32•5 = 2610 = 2,6; х₂ = 23-310 = 2.

3) (x + 2)(x – 3) = 2x(x – 4) + 6; x² – 3х + 2x – 6 = 2x² – 8х + 6;

2x² – 8х + 6 – x² + x + 6 = 0; x² – 7x + 12 = 0;

D = (–7)² – 4 • 1 • 12 = 1; D = 1;

х₁ = 7+12 = 4; х₂ = 7-12 = 3.

4) х(х – 1) – (x – 3)(x + 3) = (x + 2)² – 1;

x² – x – (x² – 9) = x² + 4x + 4 – 1; x² + 4x + 3 = x² – x – x² + 9;

x² + 4x + 3 + x – 9 = 0; x² + 5x – 6 = 0;

D = 5² – 4 • 1 • (–6) = 25 + 24; D = 7;

х₁ = -5+72 = 1; х₂ = -5+72 = –6.