Question

Tìm Max

-|x-30|-|y-4|+2019(x,y thuộc Z)

Answer 1

tìm max hay tìm min bạn

Answer 2

ta có: \(-\left|x-30\right|-\left|y-4\right|=-\left(\left|x-30\right|+\left|y-4\right|\right)\)

mà\(\left|x-30\right|+\left|y-4\right|\ge0\forall x,y\)

\(\Rightarrow-\left(\left|x-30\right|+\left|y-4\right|\right)\le0\forall x,y\)

hay\(-\left|x-30\right|-\left|y-4\right|\le0\forall\)

\(\Rightarrow-\left|x-30\right|-\left|y+4\right|+2019\le2019\)

Dấu bằng xảy ra khi:

\(-\left|x-30\right|-\left|y-4\right|=0\)

\(\Rightarrow\hept{\begin{cases}x-30=0\\y-4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=30\\y=4\end{cases}}}\)

        

Answer 3

bổ sung nha vậy max -|x-30|-|y-4|+2019 là 2019

Answer 4

bổ sung lại

max\(\text{-|x-30|-|y-4|+2019}=2019\Leftrightarrow x=30;y=4\)