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