Example 3:          The sum of two numbers is 6 and their product is 7.  What are those numbers?

Solution: 

If one of the numbers is x, then the other must be 6 – x since they add to 6.  If their product is 7, then we have the equation x(6 – x) = 7.

Expanding gives 6x – x² = 7.  If we subtract 7 from both sides, we get :

                              –x² + 6x – 7 = 0

Whenever an equation begins with a negative x², it is best to multiply both sides by negative one so it begins with a positive x².  So we do that and get:

                             x² – 6x + 7 = 0

Now we use the quadratic formula:

 

                            

                            

                            

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