Giải đáp:$x = 26$ Lời giải và giải thích chi tiết: $\begin{array}{l}Dkxd:x \ge 1\\\sqrt {x – 2\sqrt {x – 1} } – 3 = 1\\ \Leftrightarrow \sqrt {x – 1 – 2\sqrt {x – 1} + 1} = 4\\ \Leftrightarrow \sqrt {{{\left( {\sqrt {x – 1} – 1} \right)}^2}} = 4\\ \Leftrightarrow \left| {\sqrt {x – 1} – 1} \right| = 4\\ \Leftrightarrow \left[ \begin{array}{l}\sqrt {x – 1} – 1 = 4\\\sqrt {x – 1} – 1 = – 4\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}\sqrt {x – 1} = 5\\\sqrt {x – 1} = – 3\left( {ktm} \right)\end{array} \right.\\ \Leftrightarrow x – 1 = 25\\ \Leftrightarrow x = 26\left( {tm} \right)\\Vậy\,x = 26\end{array}$
Dkxd:x \ge 1\\
\sqrt {x – 2\sqrt {x – 1} } – 3 = 1\\
\Leftrightarrow \sqrt {x – 1 – 2\sqrt {x – 1} + 1} = 4\\
\Leftrightarrow \sqrt {{{\left( {\sqrt {x – 1} – 1} \right)}^2}} = 4\\
\Leftrightarrow \left| {\sqrt {x – 1} – 1} \right| = 4\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt {x – 1} – 1 = 4\\
\sqrt {x – 1} – 1 = – 4
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt {x – 1} = 5\\
\sqrt {x – 1} = – 3\left( {ktm} \right)
\end{array} \right.\\
\Leftrightarrow x – 1 = 25\\
\Leftrightarrow x = 26\left( {tm} \right)\\
Vậy\,x = 26
\end{array}$