Với \(\forall x\) ta có :
\(B=\left|x-2010\right|+\left|x-2011\right|+\left|x-2012\right|\)
\(\Leftrightarrow B=\left|x-2010\right|+\left|2011-x\right|+\left|x-2012\right|\)
\(\Leftrightarrow B\ge\left|x-2010\right|+\left|2011-x+x-2012\right|\)
\(\Leftrightarrow B\ge\left|x-2010\right|+1\)
Lại có : \(\left|x-2010\right|\ge0\)
\(\Leftrightarrow\left|x-2010\right|+1\ge1\)
Dấu "=" xảy ra khi \(\Leftrightarrow\left|x-2010\right|=0\)
\(\Leftrightarrow x=2010\)
Vậy \(A_{Min}=1\Leftrightarrow x=2010\)
Oh!!!!!!!! T nhớ t nói làm lại bài này cho Hằng mak quên nè:v
\(L=\left|x-2010\right|+\left|x-2011\right|+\left|x-2012\right|\)
\(L=\left|x-2010\right|+\left|2012-x\right|+\left|x-2011\right|\)
\(L\ge\left|x-2010+2012-x\right|+\left|x-2011\right|\)
\(L\ge2+\left|x-2011\right|\ge2\)
Dấu "=" khi: \(\left\{{}\begin{matrix}2010\le x\le2012\\x=2011\end{matrix}\right.\Leftrightarrow x=2011\)