SOLUTION: The sum of the squares of two consecutive integers is nine less than ten times the sum of the integers. find all such integers

Question 631245: The sum of the squares of two consecutive integers is nine less than ten times the sum of the integers. find all such integers
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!
n, n+1
n^2 + (n+1)^2 = 10(n + n + 1) - 9
n^2 + n^2 + 2n + 1 = 10(2n + 1) - 9
2n^2 + 2n + 1 = 20n + 10 - 9
2n^2 - 18n + 1 = 1
2n^2 - 18n = 0
2n(n - 9) = 0
n = 0, 9
answers: 0, 1 and 9, 10
CHECK:
0^2 + 1^2 = 10(0+1) - 9
1 = 1
9^2 + 10^2 = 10(9 + 10) - 9
81 + 100 = 10(19) - 9
181 = 181
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