A) \[19\]
B) \[28\]
C) \[38\]
D) \[18\]
Correct Answer: D
Solution :
\[\because \] \[{{\left( x+\frac{1}{x} \right)}^{2}}={{x}^{2}}+\frac{1}{{{x}^{2}}}+2\times x\times \frac{1}{x}\] \[=7+2=9\] \[\therefore \] \[\left( x+\frac{1}{x} \right)=\sqrt{9}=3\] Cubing both sides \[{{\left( x+\frac{1}{x} \right)}^{3}}={{(3)}^{3}}\] \[\Rightarrow \] \[{{x}^{3}}+\frac{1}{{{x}^{3}}}+3\times x\times \frac{1}{x}\left( x+\frac{1}{x} \right)=27\] \[\Rightarrow \] \[{{x}^{3}}+\frac{1}{{{x}^{3}}}+3\times 3=27\] \[\Rightarrow \] \[{{x}^{3}}+\frac{1}{{{x}^{3}}}=27-9=18\]
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