SOLUTION: The sum of the reciprocals of two consecutive even integers is 23/264 . Find the two integers.

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Question 1204547: The sum of the reciprocals of two consecutive even integers is 23/264
. Find the two integers.
Found 3 solutions by math_tutor2020, Alan3354, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = first even integer
x+2 = second even integer just after x.

Their reciprocals add to 23/264.


















Use the quadratic formula from here.
a = 23, b = -482, c = -528










or

or

or

or
Ignore the non-integer result.

Therefore,


Answer: The two consecutive even integers are 22 and 24.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The sum of the reciprocals of two consecutive even integers is 23/264
. Find the two integers.
-------------
23/264 = 46/528
--- close to 23
---> 22 & 24
Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
.

I will use an idea, which is close to Alan' solution, but is slightly different.


If the sum of the reciprocals of two consecutive even integers is 23/264,

then each reciprocal is close to   = .


Hence, each of the two consecutive even integer is close to   = 22.96.


From it, I conclude that the two consecutive even integer numbers are 22 and 24.


Now it is a matter of arithmetic to check that it is true.

Solved.



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