The product of two numbers is 28. What is the minimum value of their sum

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justaguide eNotes educator| Certified Educator

The product of two numbers is equal to 28. If one of the numbers is represented by x, the value of the other number is `28/x` .

This gives the sum of the numbers as `S = x + 28/x` .

To determine the minimum value of the sum solve S' = 0 for x; also, the value of S'' for the particular solution of x should be positive.

`S' = 1 - 28/x^2`

`1 - 28/x^2 = 0`

=> `x^2 = 28`

=> `x = +-sqrt 28`

`S'' = 56/x^3`

This is positive for `x = sqrt 28`

The minimum value of the `2*sqrt 28`