Lớn nhất nhé bạn :D
\(A=\dfrac{1}{\left|x-y\right|+\left|y-z\right|+\left|z-x\right|+2016}\)
\(\left\{{}\begin{matrix}\left|x-y\right|\ge0\\\left|y-z\right|\ge0\\\left|z-x\right|\ge0\end{matrix}\right.\) \(\Rightarrow\left|x-y\right|+\left|y-z\right|+\left|z-x\right|\ge0\)
\(\Rightarrow\left|x-y\right|+\left|y-z\right|+\left|z-x\right|+2016\ge2016\)
\(A=\dfrac{1}{\left|x-y\right|+\left|y-z\right|+\left|z-x\right|+2016}\le\dfrac{1}{2016}\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left|x-y\right|=0\\\left|y-z\right|=0\\\left|z-x\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=y\\y=z\\z=x\end{matrix}\right.\)
\(\Rightarrow x=y=z\)
