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Question 569673: The sum of reciprocals of two consecutive even numbers is 5/12,find the numbers.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The sum of reciprocals of two consecutive even numbers is 5/12,find the numbers.
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Let n = the smaller number
Then n+2 = the other number
Given: sum of the reciprocals is 5/12
1/n + 1/(n+2) = 5/12
((n+2)+n)/(n(n+2)) = 5/12
Cross-multiply and collect terms:
12(2n+2) = 5n(n+2)
This gives 5n^2 - 14n - 24 = 0
This expression can be factored as
(5n+6)(n-4) = 0
This gives n = -6/5 [not an integer] and n = 4
So the two numbers are 4 and 6
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