Question

tim gia tri lon nhat :

D=\(\dfrac{2\left|x\right|+3}{3\left|x\right|-1}\)

Answer 1

help me!

Answer 2

\(D=\dfrac{2\left|x\right|+3}{3\left|x\right|-1}\)

\(\left\{{}\begin{matrix}\left|x\right|\ge0\Rightarrow2\left|x\right|\ge0\Rightarrow2\left|x\right|+3\ge3\\\left|x\right|\ge0\Rightarrow3\left|x\right|\ge0\Rightarrow3\left|x\right|-1\ge-1\end{matrix}\right.\)

\(MAX_D\Rightarrow D\in Z^+\)

Chắc chắn: \(2\left|x\right|+3\in Z^+\)

\(\Rightarrow3\left|x\right|-1\in Z^+\)

\(MAX_D\Rightarrow MIN_{3\left|x\right|-1}\)

\(\Rightarrow3\left|x\right|-1=1\)

\(\Rightarrow3\left|x\right|=2\Rightarrow\left|x\right|=\dfrac{2}{3}\)

\(\Rightarrow MAX_D=\dfrac{2\left|\dfrac{2}{3}\right|+3}{3\left|\dfrac{2}{3}\right|-1}=\dfrac{\dfrac{13}{3}}{1}=\dfrac{13}{3}\)