Question

Решите уравнение
6/x-2+5/x=3​

Answer 1

Объяснение:

$\frac{6}{x - 2} + \frac{5}{x} = 3 \\ \frac{6x + 5(x - 2)}{x(x - 2)} = 3 \\ \frac{6x + 5x - 10}{x(x - 2)} = 3 \\ \frac{11x - 10}{x(x - 2)} = 3 \\ 11x - 10 = 3 {x}^{2} - 6x \\ - 3 {x}^{2} + 17x - 10 = 0 \\ d = (17 {)}^{2} - 4 \times ( - 3) \times ( - 10) = 289 - 120 = 169 \\ \\ x1 = \frac{ - 17 + 13}{ - 6} = \frac{ - 4}{ - 6} = \frac{2}{3} \\ x2 = \frac{ - 17 - 13}{ - 6} = \frac{ - 30}{ - 6} = 5$