Відповіді до вправ § 20 - § 26: 24.25

24.25 Обчисліть значення дробу:

1) 2x2+ 9x-5x2+ 8x+15 = 2x- 12(x+5)x+3(x+5) = 2x-1x+3.

2x² + 9x – 5 = 0; D = 9² – 4 • 2 • (–5) = 121; D = 11;

x₁ = -9+112 • 2 = 12; x₂ = -9-114 = –5.

x² + 8x + 15 = 0; D = 8² – 4 • 15 = 4;

x₁ = -8+22 = –3; x₂ = -8-22 = –5.

Якщо х = 97, то 2x-1x+3 = 2 • 97-197+3 = 193100 = 1,93.

2) 3x2- 24x + 487x-3x2+ 20 = 3(x-4)2-3x-4(x+ 53) = x-4-(x+ 53) = x-4-(x+ 53) = 4-xx+ 53.

3x² – 24x + 48 = 3(x² – 8x + 16) = 3(x – 4)²;

7x – 3x² + 20 = 3x² – 7x – 20 = 0;

D = (–7)² – 4 • 3 • (–20) = 289; D = 17;

x₁ = 7+176 = 4; x₂ = 7-176 = –106 = –52.

Якщо х = –23, то 4-xx+ 53 = 4+ 23-23+ 53 = 423.