\(\Leftrightarrow16x^4-4x^2-4xy+y^2+1=0\)
\(\Leftrightarrow\left(16x^4-8x^2+1\right)+\left(4x^2-4xy+y^2\right)=0\)
\(\Leftrightarrow\left(4x^2-1\right)^2+\left(2x-y\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x^2-1=0\\2x-y=0\end{matrix}\right.\)
\(\Leftrightarrow\left(x;y\right)=\left(-\dfrac{1}{2};-1\right);\left(\dfrac{1}{2};1\right)\)