Đáp án:
\(x \ge 3 + 2\sqrt 2 \)
Giải thích các bước giải:
\(\begin{array}{l}
DK:\left\{ \begin{array}{l}
x \ge 0\\
x - 2\sqrt x - 1 \ge 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x \ge 0\\
x - 2\sqrt x + 1 \ge 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x \ge 0\\
{\left( {\sqrt x - 1} \right)^2} \ge 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x \ge 0\\
\left| {\sqrt x - 1} \right| \ge \sqrt 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x \ge 0\\
\left[ \begin{array}{l}
\sqrt x - 1 \ge \sqrt 2 \\
\sqrt x - 1 \le - \sqrt 2
\end{array} \right.
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x \ge 0\\
\left[ \begin{array}{l}
\sqrt x \ge 1 + \sqrt 2 \\
\sqrt x \ge 1 - \sqrt 2 \left( {KTM} \right)
\end{array} \right.
\end{array} \right.\\
\to x \ge 3 + 2\sqrt 2
\end{array}\)
