Question

Giải phương trình:

\(\sqrt{x-2\sqrt{x-3}-2}=1\)

Answer 1

\(\sqrt{x-2\sqrt{x-3}-2}=1\left(x\ge3\right)\)

\(\Leftrightarrow\sqrt{x-3-2\sqrt{x-3}+1}=1\)

\(\Leftrightarrow\sqrt{\left(\sqrt{x-3}-1\right)^2}=1\)

\(\Leftrightarrow\left|\sqrt{x-3}-1\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}-1=1\\\sqrt{x-3}-1=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=4\\x-3=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=7\left(TM\right)\\x=3\left(TM\right)\end{matrix}\right.\)

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