\(A=2x^2+2xy+y^2+4x-10\)
=>\(A=\left(x^2+2xy+y^2\right)+\left(x^2+4x+4\right)-14\)
=>\(A=\left(x+y\right)^2+\left(x+2\right)^2-14\)
Vì \(\hept{\begin{cases}\left(x+y\right)^2\ge0\\\left(x+2\right)^2\ge0\end{cases}\Rightarrow}\left(x+y\right)^2+\left(x+2\right)^2-14\ge-14\)
\(\Rightarrow A_{min}=-14\Leftrightarrow\hept{\begin{cases}\left(x+y\right)^2=0\\\left(x+2\right)^2=0\end{cases}\Leftrightarrow\hept{\begin{cases}x+y=0\\x+2=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=-2\\y=2\end{cases}}}\)
Vậy Amin=-14 tại x=-2 và y=2
\(A=\left(x^2+2xy+y^2\right)+\left(x^2+4x+4\right)-14\)
\(A=\left(x+y\right)^2+\left(x+2\right)^2-14\)
\(\Rightarrow A_{min}=-14\Leftrightarrow x=-2,y=2\)
