A) 535
B) 1030
C) 790
D) 970
Correct Answer: D
Solution :
| [d] Given,\[{{a}^{2}}+\frac{1}{{{a}^{2}}}=98\] \[\Rightarrow \] \[{{a}^{2}}\frac{1}{{{a}^{2}}}+2=100\] \[\Rightarrow \] \[{{\left( a+\frac{1}{a} \right)}^{2}}=100\] \[\Rightarrow \] \[a+\frac{1}{a}=\sqrt{100}=10\] (i) \[\Rightarrow \] \[{{\left( a+\frac{1}{a} \right)}^{3}}={{(10)}^{3}}\] \[\Rightarrow \] \[{{a}^{3}}+\frac{1}{{{a}^{3}}}+3a.\frac{1}{a}\left( a+\frac{1}{a} \right)=1000\] \[\Rightarrow \] \[{{a}^{3}}+\frac{1}{{{a}^{3}}}+3\times 10=1000\] [from Eq. (i)] \[\therefore \]\[{{a}^{3}}+\frac{1}{{{a}^{3}}}=1000-30=970\] |
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