If $$n = 7 + 4\sqrt 3 {\text{,}}$$ then the value of $$\left( {\sqrt n + \frac{1}{{\sqrt n }}} \right)$$ is:
A. $${\text{2}}\sqrt 3 $$
B. 4
C. -4
D. $$ - 2\sqrt 3 $$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & n = 7 + 4\sqrt 3 \cr & \Rightarrow n = 4 + 3 + 4\sqrt 3 \cr & \Rightarrow n = {\left( 2 \right)^2} + {\left( {\sqrt 3 } \right)^2} + 2 \times 2 \times \sqrt 3 \cr & \Rightarrow n = {\left( {2 + \sqrt 3 } \right)^2} \cr & \Rightarrow \sqrt n = 2 + \sqrt 3 \cr & \Rightarrow \frac{1}{{\sqrt n }} = 2 - \sqrt 3 \cr & \therefore \sqrt n + \frac{1}{{\sqrt n }} \cr & = 2 + \sqrt 3 + 2 - \sqrt 3 \cr & = 4 \cr} $$Join The Discussion
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