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\(P=\left|x-2018\right|+\left|2020-x\right|+\left|x-2019\right|\)
\(P\ge\left|x-2018+2020-x\right|+\left|x-2019\right|=2+\left|x-2019\right|\ge2\)
\(\Rightarrow P_{min}=2\) khi \(x=2019\)
Đặt \(S=\left|x+2019\right|+\left|x+2020\right|+\left|x+2021\right|\)
\(=\left(\left|x+2019\right|+\left|x+2021\right|\right)+\left|x+2020\right|\)
\(=\left(\left|x+2019\right|+\left|-x-2021\right|\right)+\left|x+2020\right|\ge\left|x+2019+\left(-x-2021\right)\right|+0=0\)
Dấu " = " xảy ra \(\Leftrightarrow x=-2020\)
Vậy \(Min_S=2\)
\(D=\left|x-2019\right|+\left|x-2020\right|\)
Ta có: \(\left|x-2020\right|=\left|2020-x\right|\)
\(\Rightarrow\left|x-2019\right|+\left|x-2020\right|=\left|x-2019\right|+\left|2020-x\right|\)
\(\Rightarrow D=\left|x-2019\right|+\left|2020-x\right|\ge\left|x-2019+2020-x\right|\)
\(\Rightarrow D\ge1\)
Dấu " = " xảy ra khi và chỉ khi:
\(\left(x-2019\right)\left(2020-9\right)\le0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2019\ge0\\2020-9\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2019\le0\\2020-x\ge0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge2019\\x\ge2020\end{matrix}\right.\\\left\{{}\begin{matrix}x\le2029\\x\le2020\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow x=2020\)
Vậy ................
Ta có :
\(\left|x-2020\right|=\left|2020-x\right|\)
\(\Leftrightarrow\left|x-2019\right|+\left|x-2020\right|=\left|x-2019\right|+\left|2020-x\right|\)
\(\Leftrightarrow A=\left|x-2019\right|+\left|2020-x\right|\ge\left|x-2019+2020-x\right|\)
\(\Leftrightarrow A\ge1\)
Dấu "=" xảy ra
\(\Leftrightarrow\left(x-2019\right)\left(2020-x\right)\le0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2019\ge0\\2020-x\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2019\le0\\2020-x\ge0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge2019\\x\ge2020\end{matrix}\right.\\\left\{{}\begin{matrix}x\le2019\\x\le2020\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow x=2020\)
Vậy..
À ờm...đúng là sai thật, có thể ib mik gửi đề cho ạ