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.

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(52864) (Show Source): You can put this solution on YOUR website!
.


The numbers are n and n+1.


The equation is

     -  = .


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.

RELATED QUESTIONS
If the twice the reciprocal of the larger of two consecutive integers is subtracted from... (answered by vasumathi)

A positive integer is 5 less than another. If the reciprocal of the smaller integer is... (answered by josgarithmetic,Theo)

when the reciprocal of three times a number is subtracted from the reciprocal of the... (answered by ankor@dixie-net.com)

find two consecutive integers such that the reciprocal of the Lesser increased by three... (answered by josgarithmetic)

If 2 times the reciprocal of a number is subtracted from 3 times the number, the... (answered by ewatrrr)

If the reciprocal of 4 times a number is subtracted from the reciprocal of that number,... (answered by scott8148)