Question

Find three positive integers x, y, and z that satisfy the given conditions.

The sum is 30 and the sum of the squares is a minimum.

Answer 1

Step 1:

The three positive integers are and .

The sum of three positive integers are .

.

The sum of squares is .

Substitute in .

Apply partial derivative on each side with respect to .

The sum of squares is minimum so, set .

Step 2:

Apply partial derivative on each side with respect to .

The sum of squares is minimum so, set .

.

Comments

Contd...

Step 3:

Substitute in .

Substitute in .

Substitute and in .

The three positive integers are , and .

Solution:

The three positive integers are , and .