SOLUTION: The sum of the reciprocals of two consecutive even integers a and b is 9/40 . Find the integers.

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Question 502957: The sum of the reciprocals of two consecutive even integers a and b is
9/40
. Find the integers.
Answer by jrb1965(16) About Me  (Show Source):
You can put this solution on YOUR website!
a and b are two consecutive even integers so b = a + 2
1/a + 1/(a+2) = 9/40
Multiply all terms by (a+2)* a * 40
40(a+2) + 40a = 9(a+2)a
40a + 80 + 40a = 9a^2 + 18a
Rearrange to the quadratic 9a%5E2+-+62a+-+80+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 8
b = 10