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: Option A
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
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