What are three positive numbers whose sum is 18 and the sum of whose squares is as small as possible?

Expert Answers

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Use a tabular form to test all combinations. The lowest sum of numbers a, b and c such as a+b+c=18 is

6+6+6=18

`6^2+6^2+6^2=108`

For three different numbers, the smallest sum of squares is for:

5+6+7=18

`5^2+6^2+7^2=110`

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