SOLUTION: The sum of the reciprocals of 2 consecutive even integers is 5/12. Find the integers.

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Question 284619: The sum of the reciprocals of 2 consecutive even integers is 5/12. Find the integers.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be x & x+2

1/x +1/ x+2 =5/12
x+2+x=5X(x+2) /12
2x+2=5x^2+10x /12
24x+24 = 5x^2 +10x
5x^2-14x-24=0
5x^2-20x+6x-24=0
5x(x-4)+6(x-4)=0
(x-4)(5x+6)=0
x= 4
The numbers are 4 & 6