Вправи: 762 (1)

762. Розв’яжіть рівняння:

1) x(x + 1) = 56;

x² + x – 56 = 0№

D = 1² – 4 • 1 • (–56) = 1 + 224 = 225;

х₁ = -1-2252•1 = -1-152 = -162 = –8;

х₂ = -1+2252•1 = -1+ 152 = 142 = –7.

Відповідь: –8; 7.

2) (y – 2)(y – 1) = 5;

2y² – y – 4y + 2 – 5 = 0;

2y² – 5y – 3 = 0;

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

у₁ = 5-492•2 = 5-74 = -24 = –12 = –0,5;

у₂ = 5+492•2 = 5+ 74 = 124 = 3.

Відповідь: –0,5; 3.

3) 4(3 – 2z) = (z – 3)²;

12 – 8z = z² – 6z + 9;

12 – 8z – z² + 6z – 9 = 0;

–z² – 2z + 3 = 0;

D = (–2)² – 4 • (–1) • 3 = 4 + 12 = 16;

z₁ = 2-162•(-1) = 2-4-2 = -2-2 = 1;

z₂ = 2+162•(-1) = 2+4-2 = 6-2 = –3.

Відповідь: –3; 1.

4) (x + 6)(x – 2) = 2(x – 2);

x² – 2x + 6x – 12 = 2x – 4

x² + 4x – 12 – 2x + 4 = 0

x² + 2x – 8 = 0

D = 2² – 4 • 1 • (–8) = 4 + 32 = 36;

х₁ = -2-362•1 = -2-62 = -82 = –4;

х₂ = -2+362•1 = -2+ 62 = 42 = 2.

Відповідь: –4; 2.