A) 5
B) 9
C) 17
D) 7
Correct Answer: B
Solution :
\[x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\] \[=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}\] \[=\frac{\sqrt{5}+{{\sqrt{3}}^{2}}}{{{(\sqrt{5})}^{2}}-{{(\sqrt{3})}^{2}}}=\frac{5+3+2\sqrt{15}}{5-3}\] \[=\frac{8+2\sqrt{15}}{2}=4+\sqrt{15}\] \[\therefore y=4-\sqrt{15}\] \[\therefore \,\,x+y+xy=4+\sqrt{15}+4-\sqrt{15}+(4+\sqrt{15})(4-\sqrt{15)}\]\[=8+16-15=9\]
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