Вправи: 1052

1052. Скоротіть дріб:

1) 4x2- 812x2- 5x-18.

2x² – 5x – 18 = 0; D = (–5)² – 4 • 2 • (–18) = 169;

x₁ = 5+134 = 184 = 4,5; x₂ = 5-134 = –2;

4x2- 812x2- 5x-18 = 2x-9(2x+9)2x-4,5(x+2) = 2x-9(2x+9)2x-9(x+2) = 2x+9x+2.

2) 2x2+ 6x-20x3- 8.

2x² + 6x – 20 = 0; D = 36 – 4 • 2 • (–20) = 196;

x₁ = -6+144 = 2; x₂ = -6-144 = –5.

2x2+ 6x-20x2- 8 = 2x-2(x+5)x-2(x2+ 2x+4) = 2(x+5)x2+ 2x+4.

3) 2x2- 12x+182x2- x-15.

2x² – 12x + 18 = 0; D = (–12)² – 4 • 2 • 18 = 0; x₁ = x₂ = 124 = 3.

2x² – x – 15 = 0; D = (–1)² – 4 • 2 • (–15) = 121;

x₁ = 1+114 = 3; x₂ = 1-114 = –2,5.

2x2- 12x+182x2- x-15 = 2(x-3)22x-3(x+2,5) = x-3x+2,5.

4) 4x2- 11x-3-3x2+ 10x-3.

4x² – 11x – 3 = 0; D = (–11)² – 4 • 4 • (–3) = 169;

x₁ = 11+138 = 3; x₂ = 11-138 = –14.

–3x² + 10x – 3 = 0; D = 10² – 4 • (–3) • (–3) = 64;

x₁ = -10+8-6 = 13; x₂ = -10-8-6 = 3.

4x2- 11x-3-3x2+ 10x-3 = 4x-3(x+ 14)-3x-3( x- 13) = 4x+11-3x.