a/ \(\sqrt{\left(x-4\right)^2}=2x-7\)
\(\Leftrightarrow\left|x-4\right|=2x-7\) (đk: \(x\ge\frac{7}{2}\))
\(\Leftrightarrow\left[{}\begin{matrix}x-4=2x-7\\x-4=7-2x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(ktm\right)\\x=\frac{11}{3}\left(tm\right)\end{matrix}\right.\)
b/\(\sqrt{\left(2x-1\right)^2}=x+2\)
\(\Leftrightarrow\left|2x-1\right|=x+2\) (đk: \(x\ge-2\))
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=x+2\\2x-1=-x-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-\frac{1}{3}\left(tm\right)\end{matrix}\right.\)
c/ \(\sqrt{\left(x-4\right)^2}=2x+7\)
\(\Leftrightarrow\left|x-4\right|=2x+7\) (đk: \(x\ge-\frac{7}{2}\))
\(\Leftrightarrow\left[{}\begin{matrix}x-4=2x+7\\x-4=-2x-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-11\left(ktm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)
