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

Options

A. 3
B. 4
C. 5
D. 6

Answer

D

Explanation

`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.