Consecutive Odd Integers

Algebra Level 2

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.


Clarification: The odd positive integers are \( 1, 3, 5, 7, 9, \ldots.\) Two consecutive odd positive integers refer to two consecutive numbers in this sequence. It does not refer to two consecutive integers (of which one will not be odd).

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