SOLUTION: The sum of two numbers is 10 and the sum of their squares is a minimum. Algebraically determine the function that models the sum of their squares and use it to find the two numbers

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Question 395293: The sum of two numbers is 10 and the sum of their squares is a minimum. Algebraically determine the function that models the sum of their squares and use it to find the two numbers.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x = one number, 10 - x = other number
Then S%28x%29+=+x%5E2+%2B+%2810+-+x%29%5E2.
==> S%28x%29++=+2x%5E2+-+20x+%2B+100
S is minimum when x+=+-b%2F2a+=+--20%2F4+=+5.
So the two numbers are 5 and 5.