Question

In the space below, provide the larger of the two positive integers that add to 10 and have the largest possible product.

Answer 1

5

Explanation:

The integers 5 and 5 sum to 10 and have the largest possible product.

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The two numbers will be x and (10-x). Their product is x(10-x), which describes a downward-opening parabola with zeros at x=0 and x=10. The maximum (vertex) of that parabola is halfway between the zeros, at x=5. Both integers have the same value: 5. Their product is 25.

If there is a requirement the integers be distinct, then 6 and 4 are the integers of choice. Their product is 24.