If a and b are rational numbers and a + b 3 = 12 - 3 , then a : b is equal to = ?

Answer: Option A

$$\begin{array}{rl}& a+b\sqrt{3}=\frac{1}{2-\sqrt{3}}\\ & \Rightarrow \frac{1}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}\\ & \Rightarrow \frac{2+\sqrt{3}}{4-3}\\ & \Rightarrow 2+\sqrt{3}\end{array}$$
By rationalisation of denominator
⇒ a + b$$\sqrt{3}$$ = 2 + $$\sqrt{3}$$
⇒ Now compare the rational & irrational parts
∴ a = 2
   b = 1
∴ a : b
   2 : 1