Question

Решить уравнения:
5=2х-х²
10х²-2=х

Answer 1

1)
$- {x}^{2} + 2x - 5 = 0 \\ d = 4 - 4 \times ( - 1) \times ( - 5) = - 16 < 0$
здесь нет решения
2)
$10{x}^{2} - 2 - x = 0 \\ 10 {x}^{2} - x - 2 = 0 \\ d = 1 - 4 \times ( - 2) \times 10 = 81 = {9}^{2} \\ x = \frac{1 - 9}{20} = - \frac{2}{5} \\ x = \frac{1 + 9}{20} = \frac{1}{2}$
здесь ответ: х1=-2/5
х2=1/2

Answer 2

$5 = 2x - {x }^{2} \\ {x }^{2} - 2x +5 = 0 \\ d = 4-5=-1 решений нет\\ 10 {x}^{2} - 2 = x \\ 10 {x}^{2} - x - 2 = 0 \\ d = 1 - 4 \times 10 \times ( - 2 )= 81 \\ x1 = \frac{1 - 9}{20} = - \frac{8}{20} = - \frac{2}{5} = - 0.4 \\ x2 = \frac{1 + 9}{20} = \frac{10}{20} = 0.5$