SOLUTION: the sum of the reciprocals of two consecutive even integers is 9/40. what are the integers?

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Question 789857: the sum of the reciprocals of two consecutive even integers is 9/40. what are the integers?
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
consecutive even integers: x, (x+2)

1/x + 1/(x+2) = 9/40
(2x + 2)/(x(x+2)) = 9/40
40(2x + 2) = 9(x(x+2))
80x + 80 = 9x^2 + 18x
0 = 9x^2 - 62x - 80
0 = (x - 8)(9x + 10)
x = 8, x = -10/9

x must be an integer, so the integers are 8 and 10.