If $$x = \root 3 \of {2 + \sqrt 3 } {\text{,}}$$ then the value of $${x^3}{\text{ + }}\frac{1}{{{x^3}}}$$ is?
A. 8
B. 9
C. 2
D. 4
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{ }}x = \root 3 \of {2 + \sqrt 3 } \cr & {x^3} = 2 + \sqrt 3 \cr & \frac{1}{{{x^3}}} = \frac{1}{{2 + \sqrt 3 }} \times \frac{{2 - \sqrt 3 }}{{2 - \sqrt 3 }} = 2 - \sqrt 3 \cr & \therefore {x^3}{\text{ + }}\frac{1}{{{x^3}}} \cr & = 2 + \sqrt 3 + 2 - \sqrt 3 \cr & = 4 \cr} $$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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