\(\Leftrightarrow x^4-2x^2+1+2y^2-2y+\frac{1}{2}=0\)
\(\Leftrightarrow\left(x^2-1\right)^2+2\left(y-\frac{1}{2}\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2-1=0\\y-\frac{1}{2}=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\pm1\\y=\frac{1}{2}\end{matrix}\right.\)