What numbers have a sum of 13 and a product of 22?

Answer 1

Let the two numbers be a & b.

Then ab = 22 therefore b = 22/a

And, a + b = 13 . . . after substituting for b this becomes

a + (22/a) = 13 . . . multiply throughout by a.

a2 + 22 = 13a

a2 - 13a + 22 = 0 . . . this can be factored

(a - 2)(a - 11) = 0 . . .thus a = 2 or 11 and so b = 11 or 2.

The two numbers are 2 and 11.