Question

решить 1 уравнение(найти его корни)

Answer 1

$\frac{2}{5x + 1} + \frac{3}{25 {x}^{2} + 10x + 1} = 1 \\ \frac{2}{5x + 1} + \frac{3}{(5x + 1) {}^{2} } = 1 \\ 5x + 1≠0, \: x≠ - \frac{1}{5} \\ 5x + 1 = t \\ \frac{2}{t} + \frac{3}{ {t}^{2} } - 1 = 0 \\ \frac{2t+ 3 }{ {t}^{2} } - 1 = 0 \\ \frac{2t + 3 - {t}^{2} }{ {t}^{2} } = 0 \\ 2t + 3 - {t}^{2} = 0 \\ {t}^{2} - 2t - 3 = 0 \\ \left[ \begin{gathered} t_{1} = 3 \\ t_{2} = - 1 \end{gathered} \right. \rightarrow \: \left[ \begin{gathered} 5x + 1 = 3 \\ 5x + 1 = - 1 \end{gathered} \right. \\ \left[ \begin{gathered} x_{1} = \frac{2}{5} \\ x_{2} = - \frac{2}{5} \end{gathered} \right.$

Ответ: -0,4: 0,4