What two numbers add to give 6 and multiply to give 7?

Answer 1

13

Answer 2

This is equivalent to solving the simultaneous equation set {x, y: x + y = 6, xy = 7}.

By rearranging and substituting, we find that x = 6 - y, and that (6 - y)y = 7.

We can expand and simply to gain -y2 + 6y - 7 = 0, a relatively simple equation called a quadratic, and one which has a precise formula for its solution.

Using this formula, we find that y = 1.586 and y = 4.414. Note that because these add to six, we will end up with the same answers for x, i.e. for y = 1.586, x = 4.414 and ice versa.

Regardless of the way you choose to then label the numbers, the solution is (1.586, 4.414). These add to 6 and multiply to 7.