Вправи: 831

831. Розв’яжіть рівняння:

1) 10x² = 5x + 0,6; 10x² – 5x – 0,6 = 0;

D = (–5)² – 4 • 10 • (–0,6) = 25 + 24 = 49; D = 7;

x₁ = 5+ 72 •10 = 1220 = 0,6; x₂ = 5- 72 • 10 = –220 = –0,1.

2) x² + 3 = 4x; x² – 4x + 3 = 0;

D = (–4)² – 4 • 1 • 3 = 4; D = 2;

x₁ = 4+ 22 = 3; x₂ = 4- 22 = 1.

3) x² + 5x = –6; x² + 5x + 6 = 0;

D = 5² – 4 • 1 • 6 = 1; D = 1;

x₁ = -5+ 12 = -42 = –2; x₂ = -5- 12 = –3.

4) 1 – 4x = 5x²; 5x² + 4x – 1 = 0;

D = 4² – 4 • 5 • (–1) = 36; D = 6;

x₁ = -4+ 62 • 5 = 210 = 0,2; x₂ = -4- 62 • 5 = –1.

5) 81y² + 1 = –18y; 81y² + 18y + 1 = 0;

D = 18² – 4 • 81 • 1 = 0; D = 0;

y = –182 • 81 = –19.

6) 3p = 5p² – 2; 5p² – 3p – 2 = 0;

D = (–3)² – 4 • 5 • (–2) = 49; D = 7;

p₁ = 3+ 72 • 5 = 1; p₂ = 3- 72 • 5 = –0,4.