\(A=2\left(x^2+\dfrac{y^2}{4}+\dfrac{1}{4}-xy-x+\dfrac{y}{2}\right)+\dfrac{3y^2}{2}-3y+\dfrac{3}{2}+2017\)
\(A=2\left(x-\dfrac{y}{2}-\dfrac{1}{2}\right)^2+\dfrac{3}{2}\left(y-1\right)^2+2017\ge2017\)
\(\Rightarrow A_{min}=2017\) khi \(\left\{{}\begin{matrix}y-1=0\\x-\dfrac{y}{2}-\dfrac{1}{2}=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)
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