If $$\left( {2 + \sqrt 3 } \right)a$$   = $$\left( {2 - \sqrt 3 } \right)b$$   = 1 then the value of $$\frac{1}{a}$$ + $$\frac{1}{b}$$ is?

Solution (By Examveda Team)

$$\eqalign{ & \left( {2 + \sqrt 3 } \right)a = \left( {2 - \sqrt 3 } \right)b = 1 \cr & \Rightarrow \frac{1}{a} = \left( {2 + \sqrt 3 } \right) \cr & {\text{By rationals}} \cr & \Rightarrow \frac{1}{b} = \left( {2 - \sqrt 3 } \right) \cr & \Rightarrow \frac{1}{a} + \frac{1}{b} = 2 + \sqrt 3 + 2 - \sqrt 3 \cr & \Rightarrow \frac{1}{a} + \frac{1}{b} = 4 \cr} $$