# The product 2 positive numbers is 124. What is the maximum value of their sum.

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The product of two positive numbers is 124. If one of the numbers is x, the other number is `124/x` . The sum of the two numbers is `S = x + 124/x`

The first derivative of S is `S' = 1 - 124/x^2`

Solving S' = 0

=> `1 - 124/x^2 = 0`

=> `x = sqrt 124`

At `x = sqrt 124` , S'' is positive. This indicates that the value of S is minimum when `x = sqrt 124` . The maximum value that S can take on is infinity.

**The maximum value of the sum of the two numbers is infinity.**

The product of two numbers is given to be 124. Let the numbers be x and y. Now x*y = 124.

x = 124/y

As the value of x or y is decreased, the value of the other variable increases and this continues indefinitely in both the directions.

As one of the variables tends to infinity the other tends to 0. And the sum of any number and infinity is infinity. This gives the maximum value of their sum as infinity.