If x = 5 + 2√6, then what is the value of $$\sqrt x + \frac{1}{{\sqrt x }}?$$
A. 2√3
B. 3√2
C. 2√6
D. 6√2
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & x = 5 + 2\sqrt 6 \cr & \Rightarrow x = {\left( {\sqrt 3 + \sqrt 2 } \right)^2} \cr & \Rightarrow \sqrt x = \sqrt 3 + \sqrt 2 \cr & \Rightarrow \frac{1}{{\sqrt x }} = \sqrt 3 - \sqrt 2 \cr & \Rightarrow \sqrt x + \frac{1}{{\sqrt x }} = \sqrt 3 + \sqrt 2 + \sqrt 3 - \sqrt 2 \cr & \Rightarrow \sqrt x + \frac{1}{{\sqrt x }} = 2\sqrt 3 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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