SOLUTION: The difference of the reciprocals of two consecutive integers is 1/72. Find the integers.

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Question 370862: The difference of the reciprocals of two consecutive integers is 1/72. Find the integers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The difference of the reciprocals of two consecutive integers is 1/72.
Find the integers.
:
Two integers, x, (x+1)
:
1%2Fx - 1%2F%28%28x%2B1%29%29 = 1%2F72
Multiply by 72x(x+1)
results:
72(x+1) - 72x = x(x+1)
:
72x + 72 - 72x = x^2 + x
72x's cancel, a quadratic equation
x^2 + x - 72 = 0
Factor this to
(x+9)(x-8) = 0
Two solutions
x = -9, -8
and
x = +8, 9