Question

Find two positive integers such that their sum is 10, and minimize the sum of their squares.

Answer 1

Answer:

5 and 5 is the lowest answer

Step-by-step explanation:

Based on what I'm assuming from that cryptic question, I assume you are looking for two numbers that add up to 10, but have the smallest sum when they are squared and added.

So I would start with 5 and 5, because they have the best chance.

If you do anything like 3 + 7,

You will get an answer of 49 + 9, which is rather high.

2 and 8 gives you 4 + 64, which is worse.

4 and 6  gives you 16 and 36, which add to 52, which is better.

5 and 5 gives you 25 and 25, which is 50, the best choice.

Answer 2

The sum of the squares is minimum when x=y=5 and it is maximum when the numbers are 0 an 10.