A) \[\left( {{x}^{8}}-\frac{1}{{{x}^{8}}} \right)\]
B) \[\left( {{x}^{4}}-\frac{1}{{{x}^{4}}} \right)\]
C) \[\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)\]
D) \[\left( {{x}^{8}}+\frac{1}{{{x}^{8}}} \right)\]
Correct Answer: A
Solution :
(a):We have, \[\left( x-\frac{1}{x} \right)\left( x+\frac{1}{x} \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)\] \[=\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)\] \[=\left\{ {{\left( {{x}^{2}} \right)}^{2}}-{{\left( \frac{1}{{{x}^{2}}} \right)}^{2}} \right\}\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)\]You need to login to perform this action.
You will be redirected in
3 sec