Find three positive numbers x, y, and z whose sum is 30 and the sum of the squares is a minimum.
A) $x = 10 , y = 10 , z = 10$
B) $x = 2 , y = 12 , z = 16$
C) $x = 7.5 , y = 7.5 , z = 15$
D) $x = 4 , y = 6 , z = 10$
E) $x = 5 , y = 5 , z = 20$

Question

Find three positive numbers x, y, and z whose sum is 30 and the sum of the squares is a minimum. 
A) $x = 10 , y = 10 , z = 10$
B) $x = 2 , y = 12 , z = 16$
C) $x = 7.5 , y = 7.5 , z = 15$
D) $x = 4 , y = 6 , z = 10$
E) $x = 5 , y = 5 , z = 20$

Quizplus · Accepted Answer

The sum of the squares of numbers is minimized when the numbers are as close to each other as possible, given a fixed sum. Here, $x = 10, y = 10, z = 10$ equally divide the total sum of 30, minimizing the sum of their squares.

Find Three Positive Numbers X, Y, and Z Whose Sum x=10,y=10,z=10x = 10 , y = 10 , z = 10x=10,y=10,z=10

Find Three Positive Numbers X, Y, and Z Whose Sum $x = 10 , y = 10 , z = 10$