SOLUTION: The sum of the squares of three consecutive, positive integers is equal to the sum of the squares of the next two integers. What are the five integers?

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Question 197955: The sum of the squares of three consecutive, positive integers is equal to the sum of the squares of the next two integers. What are the five integers?
Answer by solver91311(24713) About Me  (Show Source):
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Let x represent the first integer. Then the next four consecutive integers are:









The sum of the squares of the first 3 is equal to the sum of the squares of the next two:









Solve the quadratic (it factors) to determine the first integer. Exclude the negative root because the problem asks for positive integers.

John