Question

угадайте корень уравнения: y+1/y=9 1/9​

Answer 1

$y + \frac{1}{y} = 9 \frac{1}{9} \\y + \frac{1}{y} = \frac{82}{9} \\ y + \frac{1}{y} - \frac{82}{9} = 0| \times 9y \\ 9 {y}^{2} - 82y + 9 = 0 \\ 9 {y}^{2} - 81y - y + 9 = 0 \\ 9y(y - 9) - (y - 9) = 0 \\ (y - 9)(9y - 1) = 0 \\ y - 9 = 0 \: \: \: 9y - 1 = 0 \\ y = 9 \: \: \: 9y = 1 \: \: \: y = \frac{1}{9}$

Ответ: y=9, y=1/9