Вправи: 934

934. Виконайте дії:

1) 1x-2 – xx2+ 2x+8.

x² + 2x – 8 = 0;

D = 2² – 4 • (–8) = 36; x₁ = -2+62 = 2; x₂ = -2-62 = –4.

1x-2 – xx2+ 2x-8 = 1x-2 – xx-2(x+4) = x+4-xx-2(x+4) = 4x-2(x+4).

2) 1x+4 + 2x2+ 6x+8.

x² + 6x + 8 = 0;

D = 6² – 4 • 8 = 4; x₁ = -6+22 = –2; x₂ = -6-22 = –4.

1x+4 + 2x2+ 6x+8 = 1x+4 + 2x+2(x+4) = x+2+2x+2(x+4) = x+4x+2(x+4) = 1x+2.

3) x+43x+2 • 3x2- 10x-8x2- 16.

3x² – 10x – 8 = 0; D = (10)² – 4 • 3 • (–8) = 196; D = 14;

x₁ = 10+146 = 4; x₂ = 10-146 = –23.

x+43x+2 • 3x2- 10x-8x2- 16 = x+4 • 3x-4(x+ 23)3x+2x-4(x+4) = 3x+23x+2 = 1 .

4) -2x2+ 5x-22x+10 : 2x2+ 5x-3x2- 25.

–2x² + 5x – 2 = 0; 2x² – 5x + 2 = 0;

D = (–5)² – 4 • 2 • 2 = 9; x₁ = 5+34 = 2; x₂ = 5-34 = 12.

2x² + 5x – 3 = 0;

D = 5² – 4 • 2 • (–3) = 49; x₁ = -5+74 = 12; x₂ = -5-74 = –3.

-2x2+ 5x-22x+10 : 2x2+ 5x-3x2- 25 = -2x-2x- 12x-5(x+5)2x+5 • 2x- 12(x+3) = x-2(5-x)2(x+3).