Повторюємо алгебру за 8 клас: 82 (1-2)

82. Скоротіть дроби:

1) x2 - x - 62x + 4 = (x - 3)(x + 2)2(x + 2) = x - 32;

x² – x – 6 = (x – 3)(x + 2);

x₁ + x₂ = 1; x₁ • x₂ = –6;

x₁ = 3; x₂ = –2.

2) 3x2 - 8x - 3x2 - 9 = (3x + 1)(x - 3)(x - 3)(x + 3) = 3x + 1x + 3;

3x² – 8x – 3 = 3(x + 13)(x – 3) = (3x + 1)(x – 3);

D = (–8)² – 4 • 3 • (–3) = 64 + 36 = 100;

x₁ = 8 - 1002 • 3 = 8 - 106 = -26 = –13.

x₂ = 8 + 106 = 186 = 3.

3) 2x2 - 3x - 2x + 1 - 2x2 = (2x + 1)(x - 2)-(2x + 1)(x - 1) = x - 21 - x.

2x² – 3x – 2 = 2(x + 12)(x – 2) = (2x + 1)(x – 2);

D = (–3)² – 4 • 2 • (–2) = 9 + 16 = 25;

x₁ = 3 - 252 • 2 = 3 - 54 = -24 = –12;

x₂ = 3 + 54 = 84 = 2.

–2x² + x + 1 = –2(x + 12)(x – 1) = –(2x + 1)(x – 1).

D = 1² – 4 • (–2) • 1 = 1 + 8 = 9;

x₁ = -1 - 92 • (-2) = -1 - 3-4 = -4-4 = 1;

x₂ = -1 + 3-4 = 2-4 = –12.