Đáp án: $x = 25$
Giải thích các bước giải:
$\begin{array}{l}
Dkxd:x \ge 0;x\# 9\\
\sqrt {{P^2} - 1} = \sqrt {2P - 1} \\
Dkxd:\left\{ \begin{array}{l}
{P^2} - 1 \ge 0\\
2P - 1 \ge 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{P^2} \ge 1\\
P \ge \dfrac{1}{2}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
P \ge 1\\
P \le - 1
\end{array} \right.\\
P \ge \dfrac{1}{2}
\end{array} \right.\\
\Leftrightarrow P \ge \dfrac{1}{2}\\
\sqrt {{P^2} - 1} = \sqrt {2P - 1} \\
\Leftrightarrow {P^2} - 1 = 2P - 1\\
\Leftrightarrow {P^2} - 2P = 0\\
\Leftrightarrow P\left( {P - 2} \right) = 0\\
\Leftrightarrow P = 2\left( {do:P \ge 1} \right)\\
Khi:\dfrac{{\sqrt x - 1}}{{\sqrt x - 3}} = 2\\
\Leftrightarrow \sqrt x - 1 = 2\sqrt x - 6\\
\Leftrightarrow \sqrt x = 5\\
\Leftrightarrow x = 25\left( {tmdk} \right)\\
Vậy\,x = 25
\end{array}$
