ĐKXĐ: \(\left\{{}\begin{matrix}x\ge3\\y\ge-3\end{matrix}\right.\)
\(\left(x+y\right)^2=4\left(x+y+2\sqrt{\left(x-3\right)\left(y+3\right)}\right)\ge4\left(x+y\right)\)
\(\Rightarrow\left[{}\begin{matrix}x+y=0\\x+y\ge4\end{matrix}\right.\)
Lại có \(\left\{{}\begin{matrix}x\ge3\\y\ge-3\end{matrix}\right.\) \(\Rightarrow\left(x+3\right)\left(y+3\right)\ge0\Rightarrow xy\ge-3\left(x+y\right)-9\)
\(P=4\left(x+y\right)^2+7xy\)
TH1: \(x+y=0\Rightarrow\left\{{}\begin{matrix}x=3\\y=-3\end{matrix}\right.\) \(\Rightarrow P=-63\)
TH2: \(x+y\ge4\)
\(P=4\left(x+y\right)^2+7xy\ge4\left(x+y\right)^2-21\left(x+y\right)-63\)
\(P\ge\left(x+y-4\right)\left[4\left(x+y\right)-5\right]-83\ge-83\)
Vậy \(P_{min}=-83\) khi \(\left\{{}\begin{matrix}x=7\\y=-3\end{matrix}\right.\)
