A) 254
B) 192
C) 292
D) 66
E) 62
Correct Answer: A
Solution :
\[\because \] \[x=8+3\sqrt{7}\] \[\therefore \] \[y=\frac{1}{8+3\sqrt{7}}=8-3\sqrt{7}\] Now, \[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=\frac{{{x}^{2}}+{{y}^{2}}}{{{(xy)}^{2}}}=\frac{{{(x+y)}^{2}}-2xy}{{{(xy)}^{2}}}\] \[={{(x+y)}^{2}}-2\] \[={{(8+3\sqrt{7}+8-3\sqrt{7})}^{2}}-2\] \[={{16}^{2}}-2=254\]You need to login to perform this action.
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