Bổ sung choChị Linh(thật ra bài này chị làm sai r nhé,đề cx sai)
\(linh= \left|x+5\right|-\left|x-2\right|\)
Áp dụng bđt: \(\left|a\right|-\left|b\right|\le\left|a-b\right|\)
\(linh=\left|x+5\right|-\left|x-2\right|\le\left|x+5-x+2\right|=7\)
Dấu "=" xảy ra khi:
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x+5\ge0\Rightarrow x\ge-5\\x-2\ge0\Rightarrow x\le2\end{matrix}\right.\\\left\{{}\begin{matrix}x+5\le0\Rightarrow x\le-5\\x-2\le0\Rightarrow x\ge2\end{matrix}\right.\end{matrix}\right.\)
Như vậy dấu "=" xảy ra khi: \(-5\le x\le2\)
Ta có: \(\left|x+5\right|-\left|x-2\right|\ge\left|x+5-x-2\right|\)
\(\Rightarrow\left|x+5\right|-\left|x-2\right|\ge\left|3\right|\)
\(\Rightarrow\left|x+5\right|-\left|x-2\right|\ge3\)
\(\Rightarrow Min_A=3\)
