\[\begin{array}{l}
{x^2} - 2x - 1 = 0\\
\Leftrightarrow {x^2} - 2x + 1 - 2 = 0\\
\Leftrightarrow {\left( {x - 1} \right)^2} = 2\\
\Leftrightarrow \left[ \begin{array}{l}
x - 1 = \sqrt 2 \\
x - 1 = - \sqrt 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \sqrt 2 + 1\\
x = - \sqrt 2 + 1
\end{array} \right.\\
Vay\,\,\,x \in \left\{ {\sqrt 2 + 1;\,\, - \sqrt 2 + 1} \right\}\,\,thi\,\,menh\,\,\,de\,\,tren\,\,dung.
\end{array}\]
