Решите уравнение: корень из (x-2)=2x-7.

\[\sqrt{x - 2} = 2x - 7\]

\[t = \sqrt{x - 2}\]

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

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

\[t_{1} = - 1;\ \ t_{2} = 1,5\]

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

\[\sqrt{x - 2} \geq 0 \Longrightarrow нет\ решения.\ \]

\[2)\ \sqrt{x - 2} = 1,5\]

\[x - 2 = 2,25\]

\[x = 4,25.\]

\[Ответ:\ 4,25.\]