what two numbers multiply to equal 30 and adds to get 21

Question

What two numbers multiply to equal 30 and adds together to equal 21

Answer 1

Call the numbers a and b. Therefore ab=30 and a+b=21. We can multiply the latter by a: a^2+30=21a, substituting for ab. The quadratic a^2-21a+30=0 can be solved using the formula, giving a=(21±sqrt(441-120))/2, so a=19.46 and 1.54. From these b=1.54 and 19.46. These identical values demonstrate the symmetry of a and b.