\(\sqrt{x-2\sqrt{x-1}}-\sqrt{x-1}=1\) ( ĐKXĐ : \(x\ge1\) )
\(\Leftrightarrow\sqrt{\left(x-1\right)-2\sqrt{x-1}+1}=1+\sqrt{x-1}\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}-1\right)^2}=\sqrt{x-1}+1\)
\(\Leftrightarrow\left|\sqrt{x-1}-1\right|=\sqrt{x-1}+1\)
Với : \(\sqrt{x-1}-1\ge0\Leftrightarrow x\ge2\)
\(\Leftrightarrow\sqrt{x-1}-1=\sqrt{x-1}+1\)
\(\Leftrightarrow0=2\left(KTM\right)\)
Với : \(\sqrt{x-1}-1< 0\Leftrightarrow x\in1\)
\(\Leftrightarrow-\sqrt{x-1}+1=\sqrt{x-1}+1\)
\(\Leftrightarrow-2\sqrt{x-1}=0\)
\(\Leftrightarrow\sqrt{x-1}=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\left(TM\right)\)
Vậy \(S=\left\{1\right\}\)
\(\sqrt{x-2\sqrt{x-1}}-\sqrt{x-1}=0\Rightarrow\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1}+1\\ \Rightarrow x-2\sqrt{x-1}=x-1+2\sqrt{x-1}+1\\ \Rightarrow x-2\sqrt{x-1}=x+2\sqrt{x-1}\\ \Rightarrow-4\sqrt{x-1}=0\Rightarrow x-1=0\Rightarrow x=1\)