The sum of two integers is 12. Rhe difference in their reciprocal is 2/9. Determine the 2 integers.

Answer 1

one number --- x
the other ----- y
x+y=12 -----> x = 12-y
x - 1/y = 2/9
12-y - 1/y = 2/9
multiply by 9y
108y - 9y^2 - 9 = 2y
9y^2 - 106y + 9 = 0
solve the quadratic, does not come out nice

Answer 2

If y is the larger number
x+y = 12
1/x - 1/y = 2/9
1/x- 1/(12-x) = 2/9
Now it ends much nicer

Answer 3

thanks, oobleck
I should really read the questions more carefully.