If $$x + \sqrt 5 = 5 + \sqrt y $$     and x, y are positive integers, then the value of $$\frac{{\sqrt x + y}}{{x + \sqrt y }}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & x + \sqrt 5 = 5 + \sqrt y \cr & {\text{Put , }}x = 5{\text{ and }}y = 5 \cr & 5 + \sqrt 5 = 5 + \sqrt 5 \cr & {\text{L}}{\text{.H}}{\text{.S}} = {\text{R}}{\text{.H}}{\text{.S}} \cr & \frac{{\sqrt x + y}}{{x + \sqrt y }} \cr & = \frac{{\sqrt 5 + 5}}{{5 + \sqrt 5 }} \cr & = 1 \cr} $$