\(A=\left|x-5\right|+\left|y+5\right|-10\)
\(\left|x-5\right|\ge0;\left|y+5\right|\ge0\)
\(A_{MIN}\Rightarrow\left|x-5\right|+\left|y+5\right|_{MIN}\)
\(\left|x-5\right|_{MIN}=0\) khi x=5
\(\left|y+5\right|_{MIN}=0\) khi y=-5
\(A_{MIM}=0+0-10=-10\)
\(A_{MIN}=-10\) khi \(x=5;y=-5\)
Ta có:
\(\left\{{}\begin{matrix}\left|x-5\right|\ge0\forall x\\\left|y+5\right|\ge0\forall x\end{matrix}\right.\)
\(\Rightarrow\left|x-5\right|+\left|y+5\right|\ge0\forall x;y\)
\(\Rightarrow\left|x-5\right|+\left|y+5\right|-10\ge-10\forall x;y\)
Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left|x-5\right|=0\\\left|y+5\right|=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=5\\y=-5\end{matrix}\right.\)
Vây GTNN của A bằng -10 \(\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=-5\end{matrix}\right.\)
