The product of two numbers is 8. Let one of the numbers be N, the other number is 8/N

The sum of the two numbers is S = N + 8/N

As the value of N is increased the value of 8/N decreases. But the sum of the two increases....

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The product of two numbers is 8. Let one of the numbers be N, the other number is 8/N

The sum of the two numbers is S = N + 8/N

As the value of N is increased the value of 8/N decreases. But the sum of the two increases. For example N = 24, 8/N = 1/3, give the product 8 but the sum is 24+1/3. The value of N can be increased forever, as it tends to infinity 8/N tends to 0 and the resulting sum of the two tends to infinity.

**There is no maximum value for the sum of the two numbers that have a product of 8, it tends to infinity.**