Відповіді до вправ § 20 - § 26: 21.12

21.12 Розв’яжіть рівняння:

1) (x – 3)² = 2x – 3; x² – 6x + 9 – 2x + 3 = 0; x² – 8х + 12 = 0;

D = (–8)² – 4 • 1 • 12 = 16; D = 4;

х₁ = 8+42 = 6; х₂ = 8-42 = 2.

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

3x² + 6x + 3 – 2x – 2 = 0; 3x² + 4x + 1 = 0;

D = 4² – 4 • 3 • 1 = 4; D = 2;

х₁ = -4+22•3 = -26 = –13; х₂ = -4-26 = –1.

3) (x + 3)(х – 1) = 2x(x – 2) + 5; x² – x + 3х – 3 = 2x² – 4x + 5;

x² + 2x – 3 – 2x² + 4x – 5 = 0; –x² + 6x – 8 = 0; x² – 6x + 8 = 0;

D = (–6)² – 4 • 1 • 8 = 4; D = 2;

х₁ = 6+22 = 4; х₂ = 6-22 = 2.

4) х(х – 3) – (x – 5)(x + 5) = (x + 1)²;

x² – 3х – (x² – 25) = x² + 2x + 1;

x² – 3х – x² + 25 = x² + 2x + 1; x² + 2x + 1 + 3х – 25 = 0;

x² + 5x – 24 = 0;

D = 5² – 4 • 1 • (–24) = 121; D = 11;

х₁ = -5+112 = 62 = 3; х₂ = -5-112 = –8.