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If x and y are positive integer satisfyi...

If x and y are positive integer satisfying `tan^(-1)((1)/(x))+tan^(-1)((1)/(y))=(1)/(7)`, then the number of ordered pairs of (x,y) is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`tan^(-1)((1)/(x))+tan^(-1)((1)/(y))=(1)/(7)`
`rArr tan^(-1)(((1)/(x)+(1)/(y))/(1-(1)/(xy)))=tan^(-1)((1)/(7))`
`rArr (x+y)/(xy-1)=(1)/(7)`
`rArr 7x+7y=xy-1`
`rArr (7-y)x=-7y-1`
`rArr x=(7y+1)/(y-7)=7+(50)/(y-7)`
Here, y = 8, 9, 12, 17, 32, 57 satisfy above equation.
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