The sum of two positive numbers is 840, what should the numbers be if their product is as large as possible?

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The sum of the two positive numbers is 840. Let one of the numbers be x, the other numbers is 840 - x. The product of the two numbers is P = (840-x)*x = 840x - x^2.

To maximize the product solve P' = 0

P' = 840 - 2x

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The sum of the two positive numbers is 840. Let one of the numbers be x, the other numbers is 840 - x. The product of the two numbers is P = (840-x)*x = 840x - x^2.

To maximize the product solve P' = 0

P' = 840 - 2x

840 - 2x = 0

=> x = 420

The product is the largest when the two numbers are the same and each is equal to 420.

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