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

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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