Відповіді до вправ § 20 - § 26: 24.23 (1)

24.23 Скоротіть дріб:

1) 4x-12x2- 5x+6 = 4(x-3)x-3(x-2) = 4x-2.

x² – 5x + 6 = 0; D = (–5)² – 4 • 6 = 1;

x₁ = 5+12 = 3; x₂ = 5-12 = 2.

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

x² – x – 12 = 0; D = (–1)² – 4 • (–12) = 49;

x₁ = 1+72 = 4; x₂ = 1-72 = –3.

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

2x² + 5x – 3 = 0; D = 5² – 4 • (–14) = 81;

x₁ = -5+92 = 2; x₂ = -5-92 = –7.

4) x2- 4x+4x2+ 5x-14 = (x-2)2x-2(x+7) = x-2x+7.

x² + 5x – 14 = 0; D = 5² – 4 • (–14) = 81;

x₁ = -5+92 = 2; x₂ = -5-92 = –7.

5) 2x2+ 9x-53x2+ 14x-5 = 2x- 12(x+5)3x- 13(x+5) = 2x-13x-1.

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

x₁ = - 9+114 = 12; x₂ = -9-114 = –5.

3x² + 14x – 5 = 0; D = 14² – 4 • 3 • (–5) = 256; D = 16;

x₁ = -14+166 = 13; x₂ = -14-166 = –5.

6) 5x2- 37x+1422x-2x2- 56 = 5x-7(x-0,4)-2x-7(x-4) = 5x-28-2x.

5x² – 37x + 14 = 0; D = (–37)² – 4 • 5 • 14 = 1089; D = 33;

x₁ = 37+3310 = 7; x₂ = 37-3310 = 0,4.

22x – 2x² – 56 = 0; x² – 11x + 28 = 0; D = (–11)² – 4 • 28 = 9;

x₁ = 11+32 = 7; x₂ = 11-32 = 4.