Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 614

\[\boxed{\mathbf{614}\mathbf{.}}\]

\[1)\ arctg\ (5x - 1) = \frac{\pi}{4}\]

\[\text{arctg\ }(5x - 1) = arctg\ 1\]

\[5x - 1 = 1\]

\[5x = 2\]

\[x = \frac{2}{5}\]

\[x = 0,4\]

\[Ответ:\ \ x = 0,4\]

\[2)\ arctg\ (3 - 5x) = - \frac{\pi}{3}\]

\[\text{arctg\ }(3 - 5x) = arctg\ \left( - \sqrt{3} \right)\]

\[\text{arctg\ }(3 - 5x) = - arctg\ \left( \sqrt{3} \right)\]

\[3 - 5x = - \sqrt{3}\]

\[5x = 3 + \sqrt{3}\]

\[x = \frac{3 + \sqrt{3}}{5}\]

\[Ответ:\ \ x = \frac{3 + \sqrt{3}}{5}.\]