a, ĐK: \(x\ge\frac{1}{2}\)
\(PT\Leftrightarrow\sqrt{2x-1-2\sqrt{2x-1}+1}=1\)
\(\Leftrightarrow\sqrt{\left(\sqrt{2x-1}-1\right)^2}=1\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{2x-1}-1=1\\1-\sqrt{2x-1}=1\end{matrix}\right.\Rightarrow\)\(\left[{}\begin{matrix}\sqrt{2x-1}=2\\\sqrt{2x-1}=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\frac{5}{2}\\x=\frac{1}{2}\end{matrix}\right.\)(tm)
b,ĐK: \(x\ge1\)
\(PT\Leftrightarrow\sqrt{x-1+2\sqrt{x-1}+1}=2\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}+1\right)^2}=2\)\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}=1\\\sqrt{x-1}=-3\left(l\right)\end{matrix}\right.\)\(\Rightarrow x=2\left(tm\right)\)
