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