A) \[8\sqrt{5}\]
B) \[2\sqrt{5}\]
C) \[5\sqrt{5}\]
D) \[7\sqrt{5}\]
Correct Answer: B
Solution :
\[{{\left( x+\frac{1}{x} \right)}^{3}}={{x}^{3}}+\frac{1}{{{x}^{3}}}+3\left( x+\frac{1}{x} \right)\] \[{{(\sqrt{5})}^{3}}={{x}^{3}}+\frac{1}{{{x}^{3}}}+3\,\,(\sqrt{5})\] \[\left( \therefore x+\frac{1}{x}=\sqrt{5} \right)\] \[\Rightarrow \] \[{{x}^{3}}+\frac{1}{{{x}^{3}}}=5\sqrt{5}-3\sqrt{5}=2\sqrt{5}\]
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