A) 4
B) 8
C) 12
D) 34
Correct Answer: D
Solution :
\[\because x-\frac{1}{2}=2\] \[\Rightarrow \] \[{{\left( x-\frac{1}{2} \right)}^{2}}=4\] \[\Rightarrow \] \[{{x}^{2}}-2x.\frac{1}{2}+\frac{1}{{{x}^{2}}}=4\] \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=4+2=6\] \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=6\] \[\Rightarrow \] \[{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}={{(6)}^{2}}\] \[\Rightarrow \] \[{{x}^{4}}+2+\frac{1}{{{x}^{4}}}=36\] \[\Rightarrow \] \[{{x}^{4}}+\frac{1}{{{x}^{4}}}=36-2\] \[\therefore \,\,\] \[{{x}^{4}}+\frac{1}{{{x}^{4}}}=34\]
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