If $${x^2} + \frac{1}{{{x^2}}} = \frac{{31}}{9}$$ and x > 0, then what is the value of $${x^3} + \frac{1}{{{x^3}}} = ?$$
A. $$\frac{{70}}{9}$$
B. $$\frac{{154}}{{27}}$$
C. $$\frac{{349}}{{27}}$$
D. $$\frac{{349}}{7}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {x^2} + \frac{1}{{{x^2}}} = \frac{{31}}{9} \cr & x + \frac{1}{x} = \sqrt {\frac{{31}}{9} + 2} \cr & x + \frac{1}{x} = \frac{7}{3} \cr & {x^3} + \frac{1}{{{x^3}}} = {n^3} - 3n \cr & {x^3} + \frac{1}{{{x^3}}} = {\left( {\frac{7}{3}} \right)^3} - 3 \times \frac{7}{3} \cr & {x^3} + \frac{1}{{{x^3}}} = \frac{{343}}{{27}} - 7 \cr & {x^3} + \frac{1}{{{x^3}}} = \frac{{343 - 7 \times 27}}{{27}} \cr & {x^3} + \frac{1}{{{x^3}}} = \frac{{154}}{{27}} \cr} $$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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