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If x=(2)/(sqrt(3)-sqrt(5)) and y=(2)/(sq...

If `x=(2)/(sqrt(3)-sqrt(5)) and y=(2)/(sqrt(3)+sqrt(5))`, then `x+y` = _______ .

A

3

B

`4sqrt(3)`

C

`-2sqrt(3)`

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`x=(2)/(sqrt(3)-sqrt(5)), y=(2)/(sqrt(3)+sqrt(5))`
`x+y =(2)/(sqrt(3)-sqrt(5))+(2)/(sqrt(3)+sqrt(5))`
`=(2sqrt(3)+2sqrt(5)+2sqrt(3)-2sqrt(5))/(3-5)=(4sqrt(3))/(-2)`
`(x+y)=-2sqrt(3)`
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