What 2 digits have a sum of 13 and a product of 12?

Let the two digits be represented by a and b.

a x b = 12 then, b = 12/a.

a + b = 13.........after substituting for b this becomes :-

a + 12/a = 13.....multiply throughout by a :-

a2 + 12 = 13a....re-arrange :-

a2 - 13a + 12 = 0

This factors as (a - 12)(a - 1) = 0

When a - 12 = 0 then a = 12

When a - 1 = 0 then a =1

As we have already substituted for b then b can take one of theses values and the two numbers are 1 and 12.

Note : The solution can be easily determined from the values supplied in the question but the process of finding the answer will apply to any such problem.