\(\left(2y\right)^2=4x^4-4x^3+4=\left(2x^2-x-1\right)^2+3x^2-2x+3>\left(2x^2-x-1\right)^2\)
\(\left(2y\right)^2=4x^4-4x^3+4=\left(2x^2-x+2\right)^2-9x^2+4x\le\left(2x^2-x+2\right)^2\)
\(\Rightarrow\left(2x^2-x-1\right)^2< \left(2y\right)^2< \left(2x^2-x+2\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}\left(2y\right)^2=\left(2x^2-x\right)^2\\\left(2y\right)^2=\left(2x^2-x+1\right)^2\\\left(2y\right)^2=\left(2x^2-x+2\right)^2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x^2-x\right)^2=4x^4-4x^3+4\\\left(2x^2-x+1\right)^2=4x^4-4x^3+4\\\left(2x^2-x+2\right)^2=4x^4-4x^3+4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-4=0\\5x^2-2x-3=0\\9x^2-4x=0\end{matrix}\right.\) \(\Rightarrow x=\left\{-2;0;1;2\right\}\) \(\Rightarrow y=...\)
