SOLUTION: The difference between the reciprocal of two cosecutive positive even number is 1/12. Find the two numbers.

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Question 191638: The difference between the reciprocal of two cosecutive positive even number is 1/12. Find the two numbers.
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let n and n+1 be the two consecutive numbers.
Then 1%2Fn+-1%2F%28n%2B1%29=1%2F12
Solving for n, we have
12%28n%2B1+-n%29+=+n%28n%2B1%29
12=n%5E2%2Bn
n%5E2%2Bn-12=0
%28n%2B4%29%28n-3%29=0
so n= -4, or n=3
If n= -4, the two consecutive numbers are -4, -3.
If n = 3, the two consecutive numbers are 3, 4.