SOLUTION: The sum of the reciprocals of two consecutive even integers a and b is 7 over 24 . Find the integers.

Question 505266: The sum of the reciprocals of two consecutive even integers a and b is
7 over 24
.
Find the integers.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The sum of the reciprocals of two consecutive even integers a and b is
7 over 24
.
Find the integers.
==============================
If they are consecutive even integers, and a is the smallest, then b = a + 2
The sum of the reciprocals = 7/24:
1/a + 1/(a+2) = 7/24
((a+2) + a)/(a(a+2)) = 7/24
(2a+2)/(a^2+2a) = 7/24
7a^2 - 34a - 48 = 0 [cross multiply and simplify]
This can be factored:
(7a+8)(a-6) = 0
Since the number is an integer, a = 6
So the other integer = 8
Ans: 6,8
Check:
1/6 + 1/8 = (3 + 4)/24 = 7/24
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