A) 18
B) 16
C) 8
D) 4
Correct Answer: D
Solution :
Given, \[{{x}^{4}}+\frac{1}{{{x}^{4}}}=322\] \[\Rightarrow \] \[{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}-2=322\] \[\Rightarrow \] \[{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}=322={{18}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=18\] \[\Rightarrow \] \[{{\left( x-\frac{1}{x} \right)}^{2}}+2=18\] \[\Rightarrow \] \[x-\frac{1}{x}=4\]
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