A) \[{{a}^{3}}+{{a}^{2}}\]
B) \[{{a}^{3}}+{{a}^{2}}-5a\]
C) \[{{a}^{3}}+{{a}^{2}}-3a-2\]
D) \[{{a}^{3}}+\text{ }{{a}^{2}}-4a-2\]
Correct Answer: C
Solution :
Given that \[x+\frac{1}{x}=a\] Then, \[{{x}^{3}}+{{x}^{2}}+\frac{1}{{{x}^{3}}}+\frac{1}{{{x}^{2}}}\] = \[\left( {{x}^{3}}+\frac{1}{{{x}^{3}}} \right)+\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\] = \[{{\left( x+\frac{1}{x} \right)}^{3}}+\left( x+\frac{1}{x} \right)+{{\left( x+\frac{1}{x} \right)}^{2}}-2\] = \[{{a}^{3}}-3a+{{a}^{2}}-2=\]
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