Question

tìm giá trị lớn nhất

-|x-100| + |y+200| -1

nhanh,đầy đủ,đúng mik tik

Answer 1

Giải:

Đặt: \(A=-\left|x-100\right|-\left|y+200\right|-1\)

Ta có:

\(\left\{{}\begin{matrix}\left|x-100\right|\ge0\\\left|y+200\right|\ge0\end{matrix}\right.\)

\(\Leftrightarrow-\left|x-100\right|-\left|y+200\right|\le0\)

\(\Leftrightarrow-\left|x-100\right|-\left|y+200\right|-1\le-1\)

\(\Leftrightarrow A\le-1\)

\(\Leftrightarrow A_{Max}=-1\)

\("="\Leftrightarrow\left\{{}\begin{matrix}x-100=0\\y+200=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=100\\y=-200\end{matrix}\right.\)

Vậy ...