Find the numbers whose sum is 10 and product is 9.
Denote the two numbers by and .
If the sum of the two numbers is 10, then .
If the product of the two numbers is 9, then .
Rearranging the second equation gives
This expression for can now be substituted into the first
Multiplying the equation by gives
Subtracting from both sides gives
This equation can be solved by factorisation.
Substituting each value for into the equation for gives
Therefore, the two numbers are 1 and 9.