\(x^2+2y^2+2xy-2x+2=0.\)
\(\Leftrightarrow\left(x^2+y^2+1+2xy-2x-2y\right)+\left(y^2+2y+1\right)=0\)
\(\Leftrightarrow\left(x+y-1\right)^2+\left(y+1\right)^2=0\)
Mà \(\left(x+y-1\right)^2\ge0,\left(y+1\right)^2\ge0\)
Suy ra \(\hept{\begin{cases}\left(x+y-1\right)^2=0\\\left(y+1\right)^2=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x+y=1\\y=-1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=2\\y=-1\end{cases}.}\)
\(2x^2-8x+y^2+2y+9=0\)
\(\Leftrightarrow\left(2x^2-8x+8\right)+\left(y^2+2y+1\right)=0\)
\(\Leftrightarrow2\left(x^2-4x+4\right)+\left(y+1\right)^2=0\)
\(\Leftrightarrow2\left(x-2\right)^2+\left(y+1\right)^2=0\)
Mà \(2\left(x-2\right)^2\ge0,\left(y+1\right)^2\ge0\)
Suy ra \(\hept{\begin{cases}2\left(x-2\right)^2=0\\\left(y+1\right)^2=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=2\\y=-1\end{cases}}}\)
