SOLUTION: Find 2 numbers whose sum is 40 if the sum of their squares is to be a minimum. What is the minimum?

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Question 424577: Find 2 numbers whose sum is 40 if the sum of their squares is to be a minimum. What is the minimum?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have two numbers, a and 40-a and want to minimize the sum a%5E2+%2B+%2840-a%29%5E2, or 2a%5E2+-+80a+%2B+1600. The parabola's leading coefficient is positive, so the minimum value occurs at the "vertex," which occurs when a+=+80%2F%282%282%29%29+=+20. Thus, {20,20} minimizes the sum and this sum is 20%5E2+%2B+20%5E2+=+800.