Find three positive numbers x, y, and z whose sum is 24 and the sum of the squares is a maximum.
A)x = y = z = 8
B)x = 4, y = 4, z = 16
C)x = 6, y = 6, z = 12
D)x = 3.2, y = 4.8, z = 8
E)x = 1.6, y = 9.6, z = 12.8

Question

Quizplus · Accepted Answer

The sum of the squares of numbers is maximized when the numbers are as close to each other as possible, given a fixed sum. This is due to the Arithmetic Mean-Quadratic Mean inequality. For a fixed sum of 24, dividing it equally among x, y, and z gives x = y = z = 8, which maximizes the sum of their squares.

Find Three Positive Numbers X, Y, and Z Whose Sum