A) \[{{x}^{6}}+\frac{1}{{{x}^{6}}}\]
B) \[{{x}^{8}}+\frac{1}{{{x}^{8}}}\]
C) \[{{x}^{8}}+\frac{1}{{{x}^{8}}}\]
D) \[{{x}^{6}}-\frac{1}{{{x}^{6}}}\]
Correct Answer: D
Solution :
\[\left( x+\frac{1}{x} \right)\left( x-\frac{1}{x} \right)\] \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}-1 \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}+1 \right)\] \[=\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)\left[ {{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}-1 \right]\] \[\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)\left( {{x}^{4}}+\frac{1}{{{x}^{4}}}+1 \right)\] \[={{x}^{6}}-\frac{1}{{{x}^{6}}}\]
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