\(\begin{array}{l}
\sqrt {x + 2\sqrt x - 1} = 2\,\,\left( {x \ge 0} \right)\\
\Rightarrow x + 2\sqrt x - 1 = 4\\
\Leftrightarrow 2\sqrt x = 5 - x\,\,\left( {x \le 5} \right)\\
\Leftrightarrow 4x = 25 - 10x + {x^2}\\
\Leftrightarrow {x^2} - 14x + 25 = 0\\
\Leftrightarrow {\left( {x - 7} \right)^2} - 24 = 0\\
\Leftrightarrow {\left( {x - 7} \right)^2} = 24\\
\Leftrightarrow \left[ \begin{array}{l}
x = 7 + 2\sqrt 6 \left( {ktm} \right)\\
x = 7 - 2\sqrt 6 \left( {tm} \right)
\end{array} \right.
\end{array}\)
