SOLUTION: the sum of the square of 2 consecutive odd positive integers is 209. find the integers.

Question 116046: the sum of the square of 2 consecutive odd positive integers is 209. find the integers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If one of the integers is n, then the other one is n + 2, and their squares are and .

Then the sum of the squares is:

Expand the binomial and simplify:

, and now you have a problem because this equation does not have rational roots, which means there is no solution to the problem as you stated it.

However, not being satisfied with that result, I did a little 'easter-egging' and discovered that and concluded that you made a small typographical error when you typed the problem.

So, let's start over:

If one of the integers is n, then the other one is n + 2, and their squares are and .

Then the sum of the squares is:

Expand the binomial and simplify:

So n = 11 or n = -13. But we can eliminate the -13 result because we are looking for consecutive odd POSITIVE integers. Therefore, the first integer is 11 and the second is 11 + 2, or 13.

Please be careful and review your input for accuracy in the future.

Hope that helps,
John

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