\[\begin{array}{l}
\sqrt {2{\rm{x}} - 3} = x - 2\\
dk:x \ge \frac{3}{2}\\
\Leftrightarrow \left\{ \begin{array}{l}
x - 2 \ge 0\\
2{\rm{x}} - 3 = {\left( {x - 2} \right)^2}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge 2\\
2{\rm{x}} - 3 = {x^2} - 4{\rm{x}} + 4
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 2}
\end{array}\\
{x^2} - 6{\rm{x}} + 7 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 2}
\end{array}\\
{x^2} - 6{\rm{x}} + 9 = 2
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 2}
\end{array}\\
{\left( {x - 3} \right)^2} = 2
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 2}
\end{array}\\
\left[ \begin{array}{l}
x - 3 = \sqrt 2 \\
x - 3 = - \sqrt 2
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 2}
\end{array}\\
\left[ \begin{array}{l}
x = 3 + \sqrt 2 \\
x = 3 - \sqrt 2
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow x = 3 + \sqrt 2 \\
vay:x = 3 + \sqrt 2
\end{array}\]