\(D=-7-\left(x+2\right)^2-\left(2-y\right)^2\)
Ta thấy: \(\left\{\begin{matrix}\left(x+2\right)^2\ge0\\\left(2-y\right)^2\ge0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}-\left(x+2\right)^2\le0\\-\left(2-y\right)^2\le0\end{matrix}\right.\)
\(\Rightarrow-\left(x+2\right)^2-\left(2-y\right)^2\le0\)
\(\Rightarrow-7-\left(x+2\right)^2-\left(2-y\right)^2\le-7\)
\(\Rightarrow D\le-7\)
Dấu "=" xảy ra khi \(\left\{\begin{matrix}-\left(x+2\right)^2=0\\-\left(2-y\right)^2=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=-2\\y=2\end{matrix}\right.\)
Vậy \(Max_D=-7\) khi \(\left\{\begin{matrix}x=-2\\y=2\end{matrix}\right.\)
c)Ta thấy: \(\left\{\begin{matrix}\left|2x-4\right|\ge0\\\left|y+2\right|\ge0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}-\left|2x-4\right|\le0\\-\left|y+2\right|\le0\end{matrix}\right.\)
\(\Rightarrow-\left|2x-4\right|-\left|y+2\right|\le0\)
\(\Rightarrow15-\left|2x-4\right|-\left|y+2\right|\le15\)
\(\Rightarrow C\le15\)
Dấu "=" xảy ra khi \(\left\{\begin{matrix}-\left|2x-4\right|=0\\-\left|y+2\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=2\\y=-2\end{matrix}\right.\)
Vậy \(Max_C=15\) khi \(\left\{\begin{matrix}x=2\\y=-2\end{matrix}\right.\)