If $$\sqrt x - \frac{1}{{\sqrt x }} = \sqrt 5 ,$$ then $${x^2} + \frac{1}{{{x^2}}}$$ is equal to:
A. 45
B. 49
C. 47
D. 51
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \sqrt x - \frac{1}{{\sqrt x }} = \sqrt 5 \cr & {\text{Square both side}} \cr & x + \frac{1}{x} - 2.x.\frac{1}{x} = 5 \cr & x + \frac{1}{x} = 5 + 2 \cr & {\text{Square both side}} \cr & {x^2} + \frac{1}{{{x^2}}} + 2.x.\frac{1}{x} = 49 \cr & {x^2} + \frac{1}{{{x^2}}} = 47 \cr} $$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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