Вправи: 1025

1025. Розв’яжіть рівняння:

1) x² = 6x – 7; x² – 6x + 7 = 0;

D = (–6)² – 4 • 7 = 8; x_1,2 = 6 ±222 = 2(3 ± 2)2 = 3 ± 2.

2) x² + 7x = –12; х² + 7x + 12 = 0;

D = 7² – 4 • 12 = 1; х₁ = -7+12 = –3; х₂ = -7-12 = –4.

3) 10x = 25x² + 1; 25x² – 10x + 1 = 0;

D = (–10)² – 4 • 25 = 0; х = 102 • 2 = 15.

4) 2 – 9х = 5x²; 5x² + 9х – 2 = 0;

D = 9² – 4 • 5 • (–2) = 121; х₁ = -9+1110 = 0,2; х₂ = -9-1110 = –2.