\(\left(\sqrt{x^2-4x+5}\right)\) \(+\left(\sqrt{9y^2-6y+1}\right)\)\(=1\)
<=>\(\left(\sqrt{\left(x-2\right)^2+1}\right)\) \(+\sqrt{\left(3y-1\right)^2}\)\(=1\)
<=>\(\left(x-2\right)^2+1+\left(3y-1\right)^2\) \(=1\)
<=>\(\left(x-2\right)^2+\left(3y-1\right)^2=0\)
<=>\(\orbr{\begin{cases}\left(x-2\right)^2=0\\\left(3y-1\right)^2=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=2\\y=\frac{1}{3}\end{cases}}\)