Two Numbers Problem: Find the Sum

What are the two numbers when their product is 713 and they differ by 8?

The sum of the two numbers is 70.

In this problem, we are given that two numbers have a product of 713 and they differ by 8. We need to find the two numbers and then calculate their sum.

Let the first number be x and the second number be y.

We can set up the following equations based on the given information:

x - y = 8 ..... Equation 1

xy = 713 ..... Equation 2

To find the values of x and y, we can solve the equations simultaneously:

From Equation 1, we have x = 8 + y

Substitute x = 8 + y into Equation 2:

y(8 + y) = 713

y^2 + 8y = 713

y^2 + 8y - 713 = 0

By factoring the quadratic equation, we get: y = -23 or y = 31

When y = 31, x = 8 + 31 = 39

Therefore, the two numbers are 31 and 39. Their sum is 70.