Вправи: 818 (1-2)

818. Скоротіть дріб:

1) 3х-13х2+2х-1 = 3х-1(3х-1)(х+1) = 1х+1;

3x² + 2x – 1 = 3(x – 13)(x + 1) = (3x – 1)(x + 1);

D = 2² – 4 • 3 • (–1) = 4 + 12 = 16.

x₁ = -2-162•3 = -2-46 = -66 = –1;

x₂ = -2+162•3 = -2+46 = 26 = 13.

2) 2х2-5х-36х-18 = (2х+1)(х-3)6(х-3) = 2х+16;

2x² – 5x – 3 = 2(x + 12)(x – 3) = (2x + 1)(x – 3);

D = (–5)² – 4 • 3 • (–3) = 25 + 24 = 49;

x₁ = 5-492•2 = 5-74 = -24 = –12;

x₂ = 5+492•2 = 5+74 = 124 = 3.

3) 16-х2х2+х-12 = (4-х)(4+х)(х+4)(х-3) = 4-хх-3;

x² + x – 12 = (x + 4)(x – 3);

x₁ + x₂ = –1; x₁ • x₂ = –12;

x₁ = –4; x₂ = 3.

4) х2-х-56х2+7х = (х+7)(х-8)х(х+7) = х-8х;

x² – x – 56 = (x + 7)(x – 8);

x₁ + x₂ = 1; x₁ • x₂ = –56;

x₁ = –7; x₂ = 8.

5) х2-3х-10х2-8х+15 = (х+2)(х-5)(х-3)(х-5) = х+2х-3;

x₁ + x₂ = 3; x₁ • x₂ = 10;

x₁ = –2; x₂ = 5.

х₃ + x₄ = 8; x₃ • x₄ = 15;

x₃ = 3; x₄ = 5.

6) х2+9х+8-х2+8х+9 = (х+1)(х+8)-(х-9)(х+1) = х+89-х;

x² + 9x + 8 = (x + 1)(x + 8);

x₁ + x₂ = –9; x₁ • x₂ = 8;

x₁ = –1; x₂ = –8.

–x² + 8x + 9 = –(x – 9)(x + 1);

D = 8² – 4 • (–1) • 9 = 64 + 36 = 100;

х₃ = -8-1002•(-1) = -8-10-2 = -18-2 = 9;

x₄ = -8+1002•(-1) = -8+10-2 = 2-2 = –1.