ĐKXĐ: ...
\(\Leftrightarrow x^2-2x+1+2\left(x-1\right)\sqrt{x-1}+x-1=4\)
\(\Leftrightarrow\left(x-1\right)^2+2\left(x-1\right)\sqrt{x-1}+x-1=4\)
\(\Leftrightarrow\left(x-1+\sqrt{x-1}\right)^2=4\)
\(\Leftrightarrow x-1+\sqrt{x-1}=2\)
\(\Leftrightarrow x-1+\sqrt{x-1}-2=0\)
\(\Leftrightarrow\left(\sqrt{x-1}-1\right)\left(\sqrt{x-1}+2\right)=0\)
\(\Leftrightarrow\sqrt{x-1}=1\)
\(\Rightarrow x=2\)