Math problem The mean of 2 numbers is 12 Find the numbers if

Math problem.

The mean of 2 numbers is 12. Find the numbers if the product is maximum.

Solution

The numbers are a and b.

Since you did not specified what kind of mean(arithmetical or geometric mean), we\'ll suppose that we have the arithmetical mean:

a + b = 2*12

a + b = 24

a = 24 - b

The product is:

P = a*b

P = (24 - b)*b

We\'ll remove the brackets and we\'ll have:

P = 24b - b^2

We\'ll consider the function P(b). For P(b) to have an extreme, P\'(b) = 0

P\'(b) = 24 - 2b

P\'(b) = 0

24 - 2b = 0

-2b = -24

b = 12

a = 24 - 12

a = 12

For the product of the numbers to be maximum, the numbers are equal:a = b = 12.