SOLUTION: Two numbers have a difference of 16. Find the numbers if their sum and product is a minimum.

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Question 906554: Two numbers have a difference of 16. Find the numbers if their sum and product is a minimum.
Answer by ichigo449(30) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be one number and y another. Then x-y = 16. Substitute y in terms of x into sum: x+(x-16) or 2x-16. Do the same with the product: x(x-16) = x^2-16x. To use a generally applicable method take the derivative of the product: 2x-16, and set equal to zero: 2x-16 = 0 or x = 8. As quadratics have a single extreme point this is sufficient to continue. Now the two numbers are: 8 and -8. Good day.