If a and b are rational numbers and $$a + b\sqrt 3 $$   $$ = $$ $$\frac{1}{{2 – \sqrt 3 }}{\text{,}}$$   then a : b is equal to = ?
a) 2 : 1
b) 2 : 3
c) $$\sqrt 3 $$ : 1
d) – $$\sqrt 3 $$ : 1

Answer: a
Explanation:
$$\eqalign{ & a + b\sqrt 3 = \frac{1}{{2 – \sqrt 3 }} \cr & \Rightarrow \frac{1}{{2 – \sqrt 3 }} \times \frac{{2 + \sqrt 3 }}{{2 + \sqrt 3 }} \cr & \Rightarrow \frac{{2 + \sqrt 3 }}{{4 – 3}} \cr & \Rightarrow 2 + \sqrt 3 \cr} $$
By rationalisation of denominator
⇒ a + b$$\sqrt 3 $$ = 2 + $$\sqrt 3 $$
⇒ Now compare the rational & irrational parts
a = 2
   b = 1
So, a : b
   2 : 1