\(A=\left|2010-x\right|+\left|x-20\right|\ge\left|2010-x+x-20\right|=1990\)
\(A_{min}=1990\) khi \(20\le x\le2010\)
\(A=\left|x-2010\right|+\left|x-20\right|\)
\(\Rightarrow A=\left|2010-x\right|+\left|x-20\right|\)
Ta có:
\(\left\{{}\begin{matrix}\left|2010-x\right|\ge2010-x\forall x\\\left|x-20\right|\ge x-20\forall x\end{matrix}\right.\)
\(\Rightarrow\left|2010-x\right|+\left|x-20\right|\ge2010-x+x-20\forall x.\)
\(\Rightarrow A\ge1990.\)
Dấu '' = " xảy ra khi:
\(\left\{{}\begin{matrix}\left|2010-x\right|=2010-x\\\left|x-20\right|=x-20\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2010-x\ge0\\x-20\ge0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2010\ge x\\x\ge20\end{matrix}\right.\Rightarrow20\le x\le2010.\)
Vậy \(MIN_A=1990\) khi \(20\le x\le1990.\)
Chúc bạn học tốt!