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Assuming the two numbers must be positive whole numbers, the answer is 1 and 11. If they need to be non-negative, it is 0 and 12.

If negative numbers are permitted (eg -1 and 13) there is no limit to the sum - ie there is no maximum.

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Q: The sum of two numbers is 12 Find the two numbers if the sum of their squares is to you a maximum?
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