Решите уравнение: корень из (x-1)=3x-7.

\[\sqrt{x - 1} = 3x - 7\]

\[t = \sqrt{x - 1}\]

\[- 3t^{2} + t + 4 = 0\]

\[3t^{2} - t - 4 = 0\]

\[t_{1} = - 1;\ \ \ t_{2} = 1\frac{1}{3}\]

\[1)\ \sqrt{x - 1} = - 1;\ \ \ \]

\[\sqrt{x - 1} \geq 0 \Longrightarrow нет\ решения;\]

\[2)\ \sqrt{x - 1} = \frac{4}{3}\]

\[x - 1 = \left( \frac{4}{3} \right)^{2}\]

\[x - 1 = \frac{16}{9}\]

\[x = 1\frac{7}{9} + 1\]

\[x = 2\frac{7}{9}\]

\[Ответ:2\frac{7}{9}\text{.\ }\]