Tìm GTNN nhé
\(A=x^2+2y^2+2xy+2y\\ A=\left(x^2+2xy+y^2\right)+y^2+2y+1-1\\ A=\left(x^2+2xy+y^2\right)+\left(y^2+2y+1\right)-1\\ A=\left(x+y\right)^2+\left(y+1\right)^2-1\)
\(\text{ Ta có : }\left(x+y\right)^2\ge0\\ \left(y+1\right)^2\ge0\\ \Rightarrow\left(x+y\right)^2+\left(y+1\right)^2\ge0\\ A=\left(x+y\right)^2+\left(y+1\right)^2-1\ge-1\)
\(\text{Dấu }"="\text{ xảy ra khi : }\left\{{}\begin{matrix}\left(y+1\right)^2=0\\\left(x+y\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y+1=0\\x+y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-1\\x-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-1\\x=1\end{matrix}\right.\)
Vậy \(A_{\left(Min\right)}=-1\) khi \(x=1\) và \(y=-1\)
Z