The average of two real numbers is 41.375 and thier product is 1668. what are the numbers?

This problem involves two unknowns, thus, it can be solved using two independent equations. We first assign a variable for each real number.

Let:

x = first real number

y = second real number

Two independent equations must then be set up which will come from the problem statement. The first equation is obtained from the statement that the average of the two real numbers is 41.375. The second equation then shows that the product of the two real numbers is equal to 1668. The equations are then:

(1) (x + y) / 2 = 41.375

(2) x*y = 1668

We then express the variable y in terms of x, such that, y = 1668/x. This is then applied in equation 1 in order to have only a single variable in the equation. After doing mathematical operations, x is then calculated to be 34.75. This value of x is then substituted in the second equation to obtain y. Finally, the two real numbers have been determined to be x = 34.75 and y = 48.