SOLUTION: The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.

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Question 724096: The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let x & x+2 be the integers

x%5E3-%28x%2B2%29%5E3+=+x%5E2%2B%28x%2B2%29%5E2+%2B400

2%28x%5E2%2Bx%5E2%2B2x%2Bx%5E2%2B4x%2B4%29=+2x%5E2%2B4x%2B404
6x%5E2%2B12x%2B8=2x%5E2%2B4x%2B404
4x%5E2%2B8x-396=0
/4
x%5E2%2B2x-99=0
(x+11)(x-9)=0
x=9 which is positive
9,11 are the positive integers