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

Solution (By Examveda Team)

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