Повторюємо алгебру за 8 клас: 81 (1-2)

81. Скоротіть дроби:

1) 4x - 12x2 - 2x - 3 = 4(x - 3)(x - 3)(x + 1) = 4x + 1.

x² – 2x – 3 = (x – 3)(x + 1);

x₁ + x₂ = 2; x₁ • x₂ = –3.

x₁ = 3; x₂ = –1.

2) x2 - 42x2 - 5x + 2 = (x - 2)(x + 2)(2x - 1)(x - 2) = x + 22x - 1.

2x² – 5x + 2 = 2(x – 12)(x – 2) = (2x – 1)(x – 2).

D = (–5)² – 4 • 2 • 2 = 25 – 16 = 9.

x₁ = 5 - 92 • 2 = 5 - 34 = 24 = 12;

x₂ = 5 + 92 • 2 = 5 + 34 = 84 = 2.

3) 2x2 + 5x - 33x - 2x2 - 1 = (2x - 1)(x + 3)-(2x - 1)(x - 1) = x + 31 - x.

2x² + 5x – 3 = 2(x – 12)(x + 3) = (2x – 1)(x + 3).

D = 5² – 4 • 2 • (–3) = 25 + 24 = 49.

x₁ = -5 - 492 • 2 = -5 - 74 = -124 = –3;

x₂ = -5 + 74 = 24 = 12.

3x – 2x² – 1 = 0;

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

D = 3² – 4 • (–2) • (–1) = 9 – 8 = 1.

x₁ = -3 - 12 • (-2) = -3 - 1-4 = -4-4 = 1.

x₂ = -3 + 1-4 = -2-4 = 12.