Problem 11

$\frac{(z+z\sqrt{xy})^2}{(x+y)(z^2+1)}+\frac{2z}{(1+z^2)\sqrt{1+z^2}}$

Given that $x,y,z$ are positive reals and $x(1-yz)=y+z$ . Find the maximum value of the expression above.

Give your answer to two decimal place.

This problem is in this Set .