SOLUTION: The sum of the reciprocals of two consecutive even integers is 7/24. Find each integer.

Question 221922: The sum of the reciprocals of two consecutive even integers is 7/24. Find each integer.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the first integer. Then

is the next consecutive even integer. The reciprocal of the first integer is then

and the reciprocal of the second is

The sum of the reciprocals is

The quadratic factors, but one of the roots is not an integer. Exclude the non-integer root. The integer root is the smaller of your two integers. Add 2 to get the other one.

John

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