If ( 2 + 3 )a = ( 2 - 3 )b = 1 then the value of 1/a + 1/b is?

Answer: Option D

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