$\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1}$
$\Rightarrow \sqrt{(\sqrt{x-1})^2-2\sqrt{x-1}+1}=\sqrt{x-1}$
$\Rightarrow \sqrt{(\sqrt{x-1}-1)^2}=\sqrt{x-1}$
Đk: $x-1\ge0\Rightarrow x\ge1$
$\Rightarrow |\sqrt{x-1}-1|=\sqrt{x-1}$
TH1:
$\sqrt{x-1}-1=\sqrt{x-1}$
$\Rightarrow -1=0$ (vô lý ) (loại)
TH2:
$ \sqrt{x-1}-1=-\sqrt{x-1}$
$\Rightarrow 2\sqrt{x-1}=1$
$\Rightarrow \sqrt{x-1}=\dfrac{1}{2}$
$\Rightarrow x-1=\dfrac{1}{4}$
$\Rightarrow x=\dfrac{5}{4}$ (tm).
