SOLUTION: The square of the largest of three consecutive integers is 320 less than the sum of the squares of the two smaller integers. find the three integers

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Question 1114873: The square of the largest of three consecutive integers is 320 less than the sum of the squares of the two smaller integers. find the three integers
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Integers n-1, n, n+1
%28n%2B1%29%5E2=%28n-1%29%5E2%2Bn%5E2-320
-
n%5E2%2B2n%2B1=n%5E2-2n%2B1%2Bn%5E2-320
2n%2B1=-2n%2B1%2Bn%5E2-320
0=-4n%2Bn%5E2-320
n%5E2-4n-320=0
n=%284%2B-+36%29%2F2
system%28n=20%2C+or%2C+n=-16%29

One or both of these should work:
-17, -16, -15
OR
19, 20, 21.