SOLUTION: the sum of the reciprocals of two consecutive integers is 11/30. find the two integers.

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Question 165633: the sum of the reciprocals of two consecutive integers is 11/30. find the two integers.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The consecutive integers are "x" and "x+1.
EQUATION:
1/x + 1/(x+1) = 11/30
30(x+1) + 30x = 11x(x+1)
60x + 30 = 11x^2+11x
11x^2 - 49x - 30 = 0
(11x + 6)(x-5) = 0
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Integer solution:
x = 5 and x+1 = 6
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Cheers,
Stan H.