Question

tìm GTLN của

C =/ x - 3,2 / - / 1,3 - x /

Answer 1

\(C=\left|x-3,2\right|-\left|1,3-x\right|\)

\(C=\left|x-3,2\right|-\left|x-1,3\right|\)

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:

\(1,3< x< 3,2\)