Find three real numbers whose sum is 22 and whose sum of squares is as small as possible

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Mathematics

Trigger

29 June, 03:48

Find three real numbers whose sum is 22 and whose sum of squares is as small as possible

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Rocketfuel · Answer 1

If the 3 numbers are the same we have 22/3 as the numbers. Sum of squares is 3*484/9=484/3=161⅓.

If we now take 7, 8 and 7 as the three numbers, sum of squares is 98+64=162 which is bigger than 161⅓.

If we take 6, 7 and 9 the sum of the squares is 36+49+81=166, bigger again.

So it would appear that the minimum sum of squares is when each number is 22/3 or 7⅓.