Why don't you put it simply? There are ten positive integers, and their sum is 24. Find the maximum and minimum of the sum of their squares.

Because they are all positive integers, the smallest square is1&; # 178; = 1

Assuming that the first nine numbers are 1, then the last number is 15, which means that the largest square number is15² =225

In this way, you count backwards.

1 1

24

39

4 16

525

636

749

864

98 1

10 100

1 1 12 1

12 144

13 169

14 196

15225

Look at the picture below. After passing the coordinate (1, 1), y=x? Significantly accelerate the growth rate

It can be seen that the larger x is, the larger its square is.

Therefore, the minimum value should appear at the position where the number 10 is evenly distributed. 24/ 10=2.4.

We bring 2 and 3 into the formula respectively.

Replace nine 2s and one 6 with 2 → 2 * 9+6 *1= 24? The result is 4*9+36* 1=72.

Replace seven 3, 3 1→3*7+ 1*3=24 with 3? The result is 9*7+ 1*3=66.

Explain that the minimum value is 66

The maximum value is naturally 15, and the other nine numbers are all equal to 1, and the result is 225+9=234.

The sum of the maximum and minimum values is 234+66=300.