\(\left\{{}\begin{matrix}u+v=1+\sqrt{2}\\3u+\sqrt{2}v=5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3u+3v=3+3\sqrt{2}\\3u=5-\sqrt{2}v\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3u=3+3\sqrt{2}-3v\\....\end{matrix}\right.\)
\(\Rightarrow3+3\sqrt{2}-3v=5-\sqrt{2}v\Rightarrow3\sqrt{2}-2=3v-\sqrt{2}v\)
\(\Rightarrow v=\dfrac{3-\sqrt{2}}{3\sqrt{2}-2}=\dfrac{1}{\sqrt{2}}\Rightarrow u=1+\dfrac{1}{\sqrt{2}}\)
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