SOLUTION: find three consecutive integers the sum of whose reciprocal is 37/60

Question 912032: find three consecutive integers the sum of whose reciprocal is 37/60

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!



Multiply through by LCD = 60x(x+1)(x+2)













Feasible rational solutions are the fractions with only 1
as a denominator (integers) since 37 is not a factor of 
any factor of 120.

Factors of 120 are 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

One solution is 4

4|37  -69 -286 -120
 |    148  316  120
  37   79   30    0



The quadratic does not factor, thus any other
solution would not be an integer.

Answer: 4,5,6

Edwin

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