Question

Решите уравнения:
а) - y2 + 5=0;
б) 8y2 + y=0;
в) 5x2 +14x - 3=0;
г) x2+6=5x;

Answer 1

Ответ:

$- {y}^{2} + 5 = 0 \\ - {y}^{2} = - 5 \\ {y}^{2} = 5 \\ y = \sqrt{5} \\ y = - \sqrt{5}$

$8 {y}^{2} + y = 0 \\ y(8y + 1) = 0 \\ y = 0 \\ 8y + 1 = 0 \\ 8y = - 1 \\ y = - \frac{1}{8}$

$5 {x}^{2} + 14x - 3 = 0 \\ a = 5 \: b = 2 \times k = 2 \times 7 \: \: c = - 3 \\ d = {k}^{2} - ac \\ d = 49 + 15 = 64 \: \: \: \sqrt{d} = 8 \\ x = \frac{ - 7 + 8}{5} = \frac{1}{5} \\ x = \frac{ - 7 - 8}{5} = - 3$

${x}^{2} + 6 = 5x \\ {x}^{2} - 5x + 6 = 0 \\ a = 1 \: \: b = - 5\: \: c = 6 \\ d = 25 - 24 = 1 \: \: \sqrt{d} = 1 \\ x = \frac{5 + 1}{2} = 3 \\ x = \frac{5 - 1}{2} = 2$