\(C=\left|x-3,2\right|-\left|1,3-x\right|\)
\(C=\left|x-3,2\right|-\left|x-1,3\right|\)
Áp dụng BĐT:
\(\left|X\right|-\left|Y\right|\le\left|X-Y\right|\)
\(\Rightarrow C\le\left|x-3,2-x+1,3\right|\)
\(C\le4,5\)
Dấu "=" xảy ra khi:
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3,2\ge0\Rightarrow x\ge3,2\\1,3-x\ge0\Rightarrow x\le1,3\end{matrix}\right.\\\left\{{}\begin{matrix}x-3,2< 0\Rightarrow x< 3,2\\1,3-x< 0\Rightarrow x>1,3\end{matrix}\right.\end{matrix}\right.\)
Vậy xảy ra khi:
\(1,3< x< 3,2\)
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