Áp dụng BĐT \(\left|a\right|-\left|b\right|\le\left|a-b\right|\) ta có :
\(\left|x-1004\right|-\left|x+1003\right|\le\left|x-1004-x-1003\right|=2007\)
Dấu \("="\) xảy ra khi \(x=-1013\)
Vậy \(GTLN=2007\) khi \(x=-1013\)
\(A=\left|x-1004\right|-\left|x+1003\right|\)
Áp dụng bất đẳng thức:
\(\left|X\right|-\left|Y\right|\le\left|X-Y\right|\)
Ta có:
\(A\le\left|x-1004-x+1003\right|\)
\(A\le1\)
Dấu "=" xảy ra khi:
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1004\ge0\Rightarrow x\ge1004\\x+1003\ge0\Rightarrow x\ge-1003\end{matrix}\right.\\\left\{{}\begin{matrix}x-1004< 0\Rightarrow x< 1004\\x+1003< 0\Rightarrow x< -1003\end{matrix}\right.\end{matrix}\right.\)
Vậy...
