Вправи: 819 (1-2)

819. Скоротіть дріб:

1) 4х+4х2-5х-6 = 4(х+1)(х+1)(х-6) = 4х-6;

x² – 5x – 6 = (x + 1)(x – 6);

x₁ + x₂ = 5; x₁ • x₂ = –6;

x₁ = –1; x₂ = 6.

2) х2-3х3х2-10х+3 = х(х-3)(3х-1)(х-3) = х3х-1;

3x² – 10x + 3 = 3(x – 13)(x – 3) = (3x – 1)(x – 3);

D = (–10)² – 4 • 3 • 3 = 100 – 36 = 64;

x₁ = 10-642•3 = 10-86 = 26 = 13;

x₂ = 10+642•3 = 10+86 = 186 = 3.

3) 5х2-4х-12х2-4 = (4х+6)(х-2)(х-2)(х+2) = 5х+6х+2;

5x² – 4x – 12 = 5(x + 65)(x – 2) = (5x + 6)(x – 2);

D = (–4)² – 4 • 5 • (–12) = 16 + 240 = 256;

x₁ = 4-2562•5 = 4-162•5 = -1210 = –65;

x₂ = 4+2562•5 = 4+1610 = 2010 = 2.