Bài toán : Cho $x,y,z \in \left(0,2\right]$ thỏa $x+y+z=3$. Chứng minh rằng :
$\frac{x}{\sqrt{y}\left(2-x\right)}+\frac{y}{\sqrt{z}\left(2-y\right)}+\frac{z}{\sqrt{x}\left(2-z\right)} \leq \frac{x}{y\left(2-x\right)}+\frac{y}{z\left(2-y\right)}+\frac{z}{x\left(2-z\right)}$