SOLUTION: the sum of three consecutive integers is one third the square of the middle number. find the integers

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Question 1087933: the sum of three consecutive integers is one third the square of the middle number. find the integers
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
n, the first of the three consecutive integers

n%2B%28n%2B1%29%2B%28n%2B2%29=%281%2F3%29%28n%2B1%29%5E2
-


3n%2B3=%281%2F3%29%28n%5E2%2B2n%2B1%29
9n%2B9=n%5E2%2B2n%2B1
n%5E2-7n-8=0
%28n%2B1%29%28n-8%29=0

the numbers
system%28n=8%2Cn%2B1=9%2Cn%2B2=10%29 

The numbers,  -1, 0, 1  also work.