Question

Find three numbers whose sum is 6 and whose sum of squares is a minimum.

Answer 1

Números que suman 6:

3 + 2 + 1 = 6=> 3^2 + 2^2 + 1^2 = 9 + 4 + 1 = 14
4 + 3 - 1 = 6 => 4^2 + 3^2 + (-1)^2 = 16 + 9 + 1 = 26 => do not use negative numbers, because that will increase the other numbers.
 
5 + 1 + 0 = 6 => 5^2  + 1 + 0 = 25 + 1 + 0 = 26

4 + 2 + 0 = 4^2 + 2^2 + 0 = 16 + 4 = 20

When you use zero the you increase the sum of the squares.

Then the three numbers that yields the minimum sum of the squares is 1, 2 and 3.