Ta có:
\(P=\left|x-1\right|+\left|x-2017\right|+\left|x-2018\right|\)
\(\Rightarrow P=\left|x-1\right|+\left|2018-x\right|+\left|x-2017\right|\)
\(\Rightarrow P\ge\left|x-1+2018-x\right|+\left|x-2017\right|\)
\(\Rightarrow P\ge2017+\left|x-2017\right|\)
\(\Rightarrow P\ge2017.\)
Dấu '' = '' xảy ra khi:
\(\left\{{}\begin{matrix}x-1\ge0\\x-2017=0\\x-2018\le0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge1\\x=2017\\x\le2018\end{matrix}\right.\Rightarrow x=2017.\)
Vậy \(MIN_P=2017\) khi \(x=2017.\)
Chúc bạn học tốt!
Ta có: \(P=\left|x-1\right|+\left|x-2017\right|+\left|x-2018\right|\)
\(\Rightarrow P=\left|x-1\right|+\left|2018-x\right|+\left|x-2017\right|\)
\(\Rightarrow P\ge\left|x-1+2018-x\right|+\left|x-2017\right|\)
\(\Rightarrow P\ge2017+\left|x-2017\right|\)
Vì \(\left|x-2017\right|\ge0\forall x\in R\)
\(\Rightarrow P\ge2017\)
Dấu = sảy ra khí: \(\left[{}\begin{matrix}x\ge1\\x=2017\\x\le2018\end{matrix}\right.\)