Question

\(\sqrt{x-2\sqrt{ }x-1}\) Tìm đk để biểu thức xđ

Answer 1

\(\sqrt{x-2\sqrt{x-1}}\text{ xác định }\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-1\ge0\\x-2\sqrt{x-1}\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x-1-2\sqrt{x-1}+1\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\\left(\sqrt{x-1}-1\right)^2\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x\ge1\end{matrix}\right.\)

\(\Leftrightarrow x\ge1\)