A) \[\frac{10\sqrt{3}}{3}\]
B) 0
C) \[3\sqrt{3}\]
D) \[6\sqrt{3}\]
Correct Answer: B
Solution :
\[{{\left( a+\frac{1}{a} \right)}^{2}}=3\] \[\Rightarrow \,\,a+\frac{1}{a}=\sqrt{3}\] Om cubing bnoth sides. \[\therefore \] \[{{\left( a+\frac{1}{a} \right)}^{3}}={{a}^{3}}+\frac{1}{{{a}^{3}}}+3\,\left( a+\frac{1}{a} \right)\] \[\Rightarrow \] \[3\sqrt{3}={{a}^{3}}+\frac{1}{{{a}^{3}}}+3\sqrt{3}\] \[\therefore \] \[{{a}^{3}}+\frac{1}{{{a}^{3}}}=0\]
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