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

Question

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

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Mathematics
2 months
2021-07-31T00:36:38+00:00
2021-07-31T00:36:38+00:00 2 Answers
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## Answers ( )

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.

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