A) 14
B) 13
C) 15
D) 10
Correct Answer: A
Solution :
\[x=\frac{\sqrt{3}+1}{\sqrt{3}-1}=\frac{{{(\sqrt{3}+1)}^{2}}}{3-1}\] \[=\frac{3+1+2\sqrt{3}}{2}=2+\sqrt{3}\] and \[y=\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{{{(\sqrt{3}-1)}^{2}}}{3-1}\] \[=\frac{3+1-2\sqrt{3}}{2}=2-\sqrt{3}\] \[\therefore \]\[{{x}^{2}}+{{y}^{2}}={{(2+\sqrt{3})}^{2}}+2{{(2-\sqrt{3})}^{2}}\] \[=4+3+4\sqrt{3}+4+3-4\sqrt{3}=7+7=14\]
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