Question

Find three positive numbers the sum of which is 27, such that the sum of their squares is as small as possible.

Answer 1

To find three positive numbers whose sum is 27 and the sum of their squares is as small as possible, we can use the concept of average.

Step-by-step explanation:

To find three positive numbers whose sum is 27 and the sum of their squares is as small as possible, we can use the concept of average.

Let's represent the numbers as x, y, and z. We know that x + y + z = 27.

Since we want the sum of their squares to be as small as possible, we can minimize the squares by choosing the numbers as close to each other as possible.

So, let's assume x = y = z.

Now, we have 3x = 27, which means x = 9. So, the three positive numbers that satisfy the conditions are 9, 9, and 9.