\(A=x^2+y^2-2x+4y+2017\)
\(=x^2-2x+1+y^2+4y+4+2012\)
\(=\left(x-1\right)^2+\left(y+2\right)^2+2012\)
Dễ thấy: \(\left\{{}\begin{matrix}\left(x-1\right)^2\ge0\\\left(y+2\right)^2\ge0\end{matrix}\right.\)
\(\Rightarrow\left(x-1\right)^2+\left(y+2\right)^2\ge0\)
\(\Rightarrow\left(x-1\right)^2+\left(y+2\right)^2+2012\ge2012\)
Xảy ra khi \(\left\{{}\begin{matrix}\left(x-1\right)^2=0\\\left(y+2\right)^2=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)
