A) 8
B) 16
C) \[2+\sqrt{15}\]
D) \[2\,\,(\sqrt{5}+\sqrt{3})\]
Correct Answer: A
Solution :
\[x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{\sqrt{5}+\sqrt{5}}{\sqrt{5}+\sqrt{3}}=\frac{{{(\sqrt{5}+\sqrt{3})}^{2}}}{5-3}\] \[=\frac{5+3+2\sqrt{15}}{2}=\frac{8+2\sqrt{15}}{2}=4+\sqrt{15}\] \[y=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}=4-\sqrt{15}\] \[\therefore \] \[x+y=4+\sqrt{15}+4-\sqrt{15}=8\]
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