If $$\frac{{{x^2} + 1}}{x} = 4\frac{1}{4},$$ then what is the value of $${x^3} + \frac{1}{{{x^3}}}?$$
A. $$\frac{{529}}{{16}}$$
B. $$\frac{{527}}{{64}}$$
C. $$\frac{{4913}}{{64}}$$
D. $$\frac{{4097}}{{64}}$$
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & \frac{{{x^2} + 1}}{x} = 4\frac{1}{4} \cr & x + \frac{1}{x} = \frac{{17}}{4} \cr & {\text{On cubing both sides,}} \cr & {\left( {x + \frac{1}{x}} \right)^3} = {\left( {\frac{{17}}{4}} \right)^3} \cr & {x^3} + \frac{1}{{{x^3}}} + 3 \times x \times \frac{1}{x}\left( {x + \frac{1}{x}} \right) = \frac{{4913}}{{64}} \cr & {x^3} + \frac{1}{{{x^3}}} + 3\left( {\frac{{17}}{4}} \right) = \frac{{4913}}{{64}} \cr & {x^3} + \frac{1}{{{x^3}}} = \frac{{4913}}{{64}} - \frac{{51}}{4} \cr & {x^3} + \frac{1}{{{x^3}}} = \frac{{4097}}{{64}} \cr} $$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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