Вправи: 638

638. Знайдіть корені рівняння:

1) (2x – 5)(х + 2) = 18; 2х² + 4х – 5х – 10 – 18 = 0;

2х² – х – 28 = 0; а = 2, b = –1, с = –28,

D = b² – 4ас = (–1)² – 4 • 2 • (–28) = 1 + 224 = 225;

D = 15; x₁ = 1+154 = 4; x₂ = 1-154 = -144 = –72 = –3,5.

Відповідь: –3,5; 4.

2) (4x – З)² + (Зx – 1)(3x + 1) = 9;

16x² – 24x + 9 + 9x² – 1 – 9 = 0; 25x² – 24x – 1 = 0;

а = 25, b = –24, с = 1,

D = b² – 4ас = (–24)² – 4 • 25 • (–1) = 576 + 100 = 676;

D – 26; x₁ = 24+2650 = 1; x₂ = 24-2650 = -250 = –125.

Відповідь: –125; 1.

3) (x + З)² – (2x – 1)² = 16; x² + 6x + 9 – (4x² – 4x + 1) = 0;

x² + 6x + 9 – 4x² + 4х – 1 – 16 = 0; –Зx² + 10x – 8 = 0;

Зx² – 10x + 8 = 0; а = З, b = –10, с = 8,

D = b² – 4ас = (–10)² – 4 • 3 • 8 = 100 – 96 = 4;

D = 2; x₁ = 10+26 = 2; x₂ = 10-26 = 86 = 42.

Відповідь: 43; 2.

4) (x – 6)² – 2x(x + 3) = 30 – 12x;

x² – 12x + 36 – 2x² – 6х – 30 + 12х = 0; –x² – 6x + 6 = 0;

x² + 6x – 6 = 0; а = 1, b = 6, с = –6,

D = b² – 4ас = 6² – 4 • 1 • (–6) = 36 + 24 = 60;

D = 60 = 215; x₁ = -6+2152 = 2(-3+ 15)2 = –3 + 15;

x₂ = -6+2152 = 2(-3- 15)2 = –3 – 15.

Відповідь: –3 + 15; –3 –15.

5) (x + 7)(х – 8) – (4x + 1)(x – 2) = –21x;

x² – 8x + 7x – 56 – (4x² – 8x + х – 2) + 21 = 0;

x² – x – 56 – 4х² + 7x + 2 + 21x = 0; –Зх² + 27x – 54 = 0;

3x² – 27x + 54 = 0; x² – 9x + 18 = 0; a = 1, b = –9, c = 18,

D = b² – 4ac = (–9)² – 4 • 18 = 81 – 72 = 9;

D = 3; x₁ = 9+32 = 6; x₂ = 9-32 = 3.

Відповідь: 3; 6.

6) (2x – 1)(2x + 1) – x(1 – x) = 2x(x + 1);

4x² – 1 – x + x² = 2x² + 2x; 4x² – 1 – x + x² – 2x² – 2x = 0; Зx² – Зx – 1 = 0; а = З, b = –3, с = –1,

D = b² – 4ас = (–3)² – 4 • 3 • (–1) = 9 + 12 = 21;

D = 21; x₁ = 3+ 216; x₂ = 3- 216.

Відповідь:3+ 216; 3- 216.