SOLUTION: The difference of the cubes of two consecutive positive integers is 217. What is the sum of the two integers?

Question 255252: The difference of the cubes of two consecutive positive integers is 217. What is the sum of the two integers?

Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Let the two consecutive integers be n and (n+1)
Given, (n+1)^3-n^3 = 217
n^3+3n^2+3n+1-n^3-217 = 0
3n^2+3n-216 = 0
n^2+n-72 = 0
(n+9)(n-8) = 0
n = 8 or -9
Taking n =8, we get the numbers are 8and 8+1 = 9
Sum of the numbers = 8+9 = 17
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