A) 2
B) 4
C) 8
D) 16
Correct Answer: A
Solution :
\[{{x}^{2}}+{{y}^{2}}+\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}-4=0\] \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-2+{{y}^{2}}+\frac{1}{{{y}^{2}}}-2=0\] \[\Rightarrow \] \[{{\left( x-\frac{1}{x} \right)}^{2}}+{{\left( y-\frac{1}{y} \right)}^{2}}=0\] \[\Rightarrow \] \[x-\frac{1}{x}=0\] \[\Rightarrow \] \[{{x}^{2}}-1=0\] \[\Rightarrow \]\[x=1\] Similarly, \[y=1\] \[\therefore \] \[{{x}^{2}}+{{y}^{2}}=1+1=2\]
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