\(Taco:\left\{{}\begin{matrix}\left|x+5\right|\ge0\\\left|y-8\right|\ge0\end{matrix}\right.\forall x,y\Rightarrow A\ge0+0+2000=2000\Rightarrow A_{min}=2000.Dấu"="xayrakhi:\left\{{}\begin{matrix}x+5=0\\y-8=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=8\end{matrix}\right.\)
+ \(\left\{{}\begin{matrix}\left|x+5\right|\ge0\forall x\\\left|y-8\right|\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow\left|x+5\right|+\left|y-8\right|\ge0\forall x,y\)
\(\Rightarrow A=\left|x+5\right|+\left|y-8\right|+2000\ge2000\forall x,y\)
\(A=2000\) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x+5\right|=0\\\left|y-8\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=8\end{matrix}\right.\)
Vậy Min A = 2000 \(\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=8\end{matrix}\right.\)
Vì \(\left|x+5\right|\ge0;\left|y-8\right|\ge0\) nên A=\(\left|x+5\right|+\left|y-8\right|+2000\ge0+0+2000\)
nên A\(\ge2000\)
Vậy GTNN của A = 2000 khi \([\frac{\left|x+5\right|=0}{\left|y-8\right|=0}\Leftrightarrow[\frac{x=-5}{y=8}\)
