$\begin{aligned}\sqrt{x+3-4\sqrt{x-1}}+ \sqrt{x+8-6\sqrt{x-1}}=1\end{aligned}$
$\begin{aligned}\sqrt{x+3-2\sqrt{4\left( x-1\right) }}+\sqrt{x+8-2\sqrt{9\left( x-1\right) }}=1\end{aligned}$
$\begin{aligned}\left| \sqrt{x-1}-2\right| +| \sqrt{x-1}-3| =1\end{aligned}$
$\begin{aligned}\sqrt{x-1} <2\Rightarrow -\sqrt{x-1}+2-\sqrt{x-1}+3= 1\end{aligned}$
$\begin{aligned} -\sqrt{x-1}+2-\sqrt{x-1}+3=1\\ -2\sqrt{x-1}=-4\\ \sqrt{x-1}=2\\ x-1=4\\ x=5\end{aligned}$
$\begin{aligned}2 <\sqrt{x-1} <3\Rightarrow \\ \sqrt{x-1}-2-\sqrt{x-1}+3=1\Rightarrow \\ 1=1\end{aligned}$
Olduğundan sonsuz tane çözüm vardır.