\(l=2010+\left|x-2011\right|+\left|x-2012\right|+\left|x-2013\right|\)
\(=2010+\left|x-2011\right|+\left|2013-x\right|+\left|x-2012\right|\)
\(\ge2010+\left|x-2011+2013-x\right|+\left|x-2012\right|\)
\(\)\(=2010+2+\left|x-2012\right|\)
\(=2012+\left|x-2012\right|\ge2012\)
Dấu "=" xảy ra khi: \(\left\{{}\begin{matrix}x-2011\ge0\\x-2012=0\\x-2013\le0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge2011\\x=2012\\x\le2013\end{matrix}\right.\Rightarrow x=2012\)
Vậy \(min_l=2012\) khi \(x=2012\)
Đúng 0
Bình luận (4)
