SOLUTION: The sum of reciprocals of two consecutive even integers is given below. 5/12. Find the integers.

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Question 446610: The sum of reciprocals of two consecutive even integers is given below.
5/12. Find the integers.
Answer by robertb(4012) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx+%2B+1%2F%28x%2B2%29+=+5%2F12
<==> %282x%2B2%29%2F%28x%28x%2B2%29%29+=+5%2F12
<==> 12%282x%2B2%29+=+5x%28x%2B2%29
<==> 24x+%2B+24+=+5x%5E2+%2B+10x
<==> 5x%5E2+-+14x+-+24+=+0
==> (x-4)(5x+6) = 0 ==> x = 4 or -6/5.
Eliminate the second value since it is not an integer.
Hence the two integers are 4 and 6.