TITLE: Math Olympiad Algebraic Question Comprising Square Roots
QUESTION [7 upvotes]: If $m$ and $n$ are positive real numbers satisfying the equation $$m+4\sqrt{mn}-2\sqrt{m}-4\sqrt{n}+4n=3$$ 
  find the value of $$\frac{\sqrt{m}+2\sqrt{n}+2014}{4-\sqrt{m}-2\sqrt{n}}$$

I came across this question in a Math Olympiad Competition and had no idea how to solve it. Can anyone help? Thanks.

REPLY [11 votes]: The trivial answer is to realize that m = 1 and n = 1 meets the first criteria, so you can use those in the second equation.
But that's not much fun.