Вправи: 960

960. Знайдіть корені рівняння:

1) x-2x = 3x+2.

(x – 2)(x + 2) = 3x,

x ≠ 0,

x ≠ –2.

x² – 3x – 4 = 0; D = (–3)² – 4 • (–4) = 25;

x₁ = 3+52 = 4; x₂ = 3-52 = –1.

2) 3x-1x+3 = xx+1.

(3x – 1)(x + 1) = x(x + 3),

x ≠ –3,

x ≠ –1.

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

D = (–1)² – 4 • 2 • (–1) = 9; x₁ = 1+34 = 1; x₂ = 1-35 = –12.

3) 34-x = x.

3 = x(4 – x),

x ≠ 4.

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

x₁ = 4+22 = 3; x₂ = 4-22 = 1.

4) 6x = 2x – 1.

6 = 2x² – x

x ≠ 0.

2x² – x – 6 = 0; D = (–1)² – 4 • 2 •(–6) = 49;

x₁ = 1+74 = 2; x₂ = 1-74 = –1,5.

Відповідь: 1) –1; 4; 2) –12; 1; 3) 1; 3; 4) –1,5; 2.