A) 144
B) 400
C) 236
D) 527
Correct Answer: D
Solution :
We have, \[x+\frac{1}{x}=5\] Squaring both sides, we get\[{{\left( x+\frac{1}{x} \right)}^{2}}=25\] \[\Rightarrow {{x}^{2}}+\frac{1}{{{x}^{2}}}+2x\times \frac{1}{x}=25\] \[\Rightarrow {{x}^{2}}+\frac{1}{{{x}^{2}}}+2=25\Rightarrow {{x}^{2}}+\frac{1}{{{x}^{2}}}=23\] Again squaring both sides, we get, \[{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}={{(23)}^{2}}\] \[\Rightarrow {{x}^{4}}+\frac{1}{{{x}^{4}}}+2{{x}^{2}}\times \frac{1}{{{x}^{2}}}=529\] \[\Rightarrow {{x}^{4}}+\frac{1}{{{x}^{4}}}=529-2\Rightarrow {{x}^{4}}+\frac{1}{{{x}^{4}}}=527\].
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