For all nonnegative real numbers $x,y$ and $z$, prove that $\dfrac{(x+y+z)^2}{3} \geq x\sqrt{yz}+y\sqrt{xz}+z\sqrt{xy}.$
Let $a,b,c$ be non-negative real numbers , then $\frac{(a+b+c)^2}{3}\ge a\sqrt{bc}+b\sqrt{ca}+c\sqrt{ab}$?