1) \(ĐK:x\ge3\)
\(\Leftrightarrow\sqrt{2x-6}=18\)
\(\Leftrightarrow2x-6=324\)
\(\Leftrightarrow2x=330\Leftrightarrow x=165\left(tm\right)\)
2) \(ĐK:x\le5\)
\(\Leftrightarrow2\sqrt{10-2x}=12\)
\(\Leftrightarrow\sqrt{10-2x}=6\)
\(\Leftrightarrow10-2x=36\Leftrightarrow2x=-26\Leftrightarrow x=-13\left(tm\right)\)
3) \(\Leftrightarrow\sqrt{\left(x-2\right)^2}=5\)
\(\Leftrightarrow\left|x-2\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=5\\x-2=-5\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-3\end{matrix}\right.\)
4) \(ĐK:x\ge-3\)
\(\Leftrightarrow\sqrt{\left(x-3\right)^2}=3+x\)
\(\Leftrightarrow\left|x-3\right|=x+3\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=x+3\\x-3=-x-3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}-3=3\left(VLý\right)\\x=0\left(tm\right)\end{matrix}\right.\)
4: Ta có: \(\sqrt{x^2-6x+9}-x=3\)
\(\Leftrightarrow\left|x-3\right|=x+3\)
\(\Leftrightarrow3-x=x+3\left(x< 3\right)\)
hay x=0