Question 25
Determine the total number of ordered pairs of positive integers $(x,y)$ satisfying the equation
$$x\sqrt{y}+y\sqrt{x}+\sqrt{2006xy}-\sqrt{2006x}-\sqrt{2006y}-2006=0.$$
$$x\sqrt{y}+y\sqrt{x}+\sqrt{2006xy}-\sqrt{2006x}-\sqrt{2006y}-2006=0.$$