A) 727
B) 772
C) 722
D) 277
Correct Answer: A
Solution :
\[\because \,\,\left( x-\frac{1}{x} \right)=5\] Squaring both sides. \[{{\left( x-\frac{1}{x} \right)}^{2}}={{(5)}^{2}}\] \[\Rightarrow \,{{x}^{2}}+\frac{1}{{{x}^{2}}}-2\times x\times \frac{1}{x}=25\] \[\Rightarrow \,{{x}^{2}}+\frac{1}{{{x}^{2}}}=25+2=27\] Squaring both sides again \[{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}={{(27)}^{2}}\] \[\Rightarrow \] \[{{x}^{4}}+\frac{1}{{{x}^{4}}}+2\times {{x}^{2}}\times \frac{1}{{{x}^{2}}}=729\] \[\Rightarrow {{x}^{4}}+\frac{1}{{{x}^{4}}}+2=729\] \[\Rightarrow {{x}^{4}}+\frac{1}{{{x}^{4}}}=729-2\] \[\Rightarrow {{x}^{4}}+\frac{1}{{{x}^{4}}}=727\]
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