\(\Leftrightarrow8x^2+2y^2-4xy-4x-2y< 2\)
\(\Leftrightarrow\left(4x^2-4xy+y^2\right)+\left(y^2-2y+1\right)+\left(4x^2-4x+1\right)< 4\)
\(\Leftrightarrow\left(2x-y\right)^2+\left(y-1\right)^2+\left(2x-1\right)^2< 4\)
\(\Rightarrow\left(2x-1\right)^2< 4-\left(2x-y\right)^2-\left(y-1\right)^2< 4\)
\(\Leftrightarrow\left(2x-1\right)^2=1\) (do \(\left(2x-1\right)^2\) luôn là SCP lẻ)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
- Với \(x=0\Rightarrow y^2-y< 1\Rightarrow\left(2y-1\right)^2< 5\)
\(\Rightarrow\left(2y-1\right)^2=1\Rightarrow\left[{}\begin{matrix}y=0\\y=1\end{matrix}\right.\)
- Với \(x=1\Rightarrow y^2-3y+1< 0\Rightarrow\left(2y-3\right)^2< 5\)
\(\Rightarrow\left(2y-3\right)^2=1\Rightarrow\left[{}\begin{matrix}y=2\\y=1\end{matrix}\right.\)
