## 2014 Singapore MO (Senior Rd 1) Problem 23

2014 SMO (Senior-Rd1) 23. Let $n$ be a positive integer, and let $x = \frac{\sqrt{n+2} - \sqrt{n}}{\sqrt{n+2} + \sqrt{n}}$ and $y = \frac{\sqrt{n+2} + \sqrt{n}}{\sqrt{n+2} - \sqrt{n}}$. It is given that $14x^2 + 26xy + 14y^2 = 2014$. Find the value of $n$.