Ta có: A\(=\)\(2x^2+y^2-2xy+4x+2y+5\)
\(=\left(x^2-2xy+y^2\right)-2\left(x-y\right)+1+\left(x^2+6x+9\right)-5\)
\(=\) \(\left(x-y\right)^2-2\left(x-y\right)+1+\left(x+3\right)^2-5\)
\(=\left(x-y-1\right)^2+\left(x+3\right)^2-5\)
Ta có: \(\left\{\begin{matrix}\left(x-y-1\right)^2\ge0\\\left(x+3\right)^2\ge0\end{matrix}\right.\)
\(\Rightarrow\left(x-y-1\right)^2+\left(x+3\right)^2\ge0\)
\(\Rightarrow\left(x-y-1\right)^2+\left(x+3\right)^2-5\ge-5\)
Hay A \(\ge-5\)
\(\Rightarrow Amin=-5\)
\(\Leftrightarrow\left\{\begin{matrix}x-y-1=0\\x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}x=-3\\y=-2\end{matrix}\right.\)
