Відповіді до вправ § 20 - § 26: 25.9 (1-2)

25.9 Знайдіть корені рівняння:

1) x-3x = 8x+3.

(x – 3)(x + 3) = 8x,

x ≠ 0,

x ≠ –3.

x² – 9 = 8x; x² – 8x – 9 = 0; D = (–8)² – 4 • (–9) = 100;

x₁ = 8+102 = 9; x₂ = 8-102 = –1.

2) 2x-3x+2 = xx+6.

(2x – 3)(x + 6) = x(x + 2),

x ≠ –2,

x ≠ –6.

2x² + 12x – 3x – 18 = x² + 2x; x² + 7x – 18 = 0;

D = 7² – 4 • (–18) = 121;

x₁ = -7+112 = 2; x₂ = -7-112 = –9.

3) 10x-3 = x.

10 = x(x – 3),

x ≠ 3.

x² – 3x – 10 = 0; D = (–3)² – 4 • (–10) = 49;

x₁ = 3+72 = 5; x₂ = 3-72 = –2.

4) 8x = 3x + 2.

8 = 3x² + 2x,

x ≠ 0.

3x² + 2x – 8 = 0; D = 2² – 4 • 3 • (–8) = 100;

x₁ = -2+106 = 86 = 113; x₂ = -2-106 = –2.

Відповідь: 1) –1; 9; 2) –9; 2; 3) –2; 5; 4) –2; 113.