SOLUTION: If 3 times the reciprocal of the larger of two consecutive integers is subtracted from 2 times the reciprocal of the smaller, then the result is 1/2. Find the two integers.

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Question 1171126: If 3 times the reciprocal of the larger of two consecutive integers is subtracted from 2 times the reciprocal of the smaller, then the result is 1/2. Find the two integers.
Answer by ikleyn(52863) About Me  (Show Source):
You can put this solution on YOUR website!
.

The numbers are n and n+1.


The equation is

    2%2Fn - 3%2F%28n%2B1%29 = 1%2F2.


Multiply both sides by 2n*(n+1).  You will get

    4(n+1) - 6n = n*(n+1)

    4n + 4 - 6n = n^2 + n

    n^2 + 3n - 4 = 0

    (n-1)*(n+4) = 0.


The roots are  n= 1  and  n= -4.


Both roots work.


ANSWER.  There are two solutions.

         First solution represents numbers 1 and 2.

         Second solution represents numbers -4 and -3.

Solved.