Question

Tìm GTLN của biểu thức : -20 - |4 - x| - 2|y + 1|

Answer 1

Ta thấy: \(\left\{\begin{matrix}\left|4-x\right|\ge0\\\left|y+1\right|\ge0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}\left|4-x\right|\ge0\\2\left|y+1\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left\{\begin{matrix}-\left|4-x\right|\le0\\-2\left|y+1\right|\le0\end{matrix}\right.\)\(\Rightarrow-\left|4-x\right|-2\left|y+1\right|\le0\)

\(\Rightarrow-20-\left|4-x\right|-2\left|y+1\right|\le-20\)

Dấu "=" xảy ra khi \(\left\{\begin{matrix}-\left|4-x\right|=0\\-2\left|y+1\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=4\\y=-1\end{matrix}\right.\)

Vậy GTLN=-20 khi \(\left\{\begin{matrix}x=4\\y=-1\end{matrix}\right.\)