Вправи: 932

932. Скоротіть дріб:

1) x2+ 6x+5x2+ 5x = x+1(x+5)x(x+5) = x+1x.

x² + 6x + 5 = 0; D = 6² – 4 • 5 = 16;

x₁ = -6+42 = –1; x₂ = -6-42 = –5.

2) x2- 163x2- 10x-8 = x-4(x+4)3x-4(x+ 23) = x+43x+2.

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

x₁ = 10+146 = 4; x₂ = 10-146 = –23.

3) x2+ x-6x2- 7x+10 = x-2(x+3)x-5(x-2) = x+3x-5.

x² + x – 6 = 0; D = 1² – 4 • (–6) = 25;

x₁ = -1+52 = 2; x₂ = -1-52 = –3.

x² – 7x + 10 = 0; D = (–7)² – 4 • 10 = 9;

x₁ = 7+32 = 5; x₂ = 7-32 = 2.

4) 2x2+ 4x+23x2- 6x-9 = 2(x+1)23x-3(x+1) = 2(x+1)3(x-3).

2x² + 4x + 2 = 2(x² + 2x + 1) = 2(x + 2)²;

3x² – 6x – 9 = 0; x² – 2x – 3 = 0; D = (–2)² – 4 • (–3) = 16;

x₁ = 2+42 = 3; x₂ = 2-42 = –1.