Question

What two numbers add to get 31 and multiply to get 140

Answer 1

x+y = 31 ---> y = 31-x

xy = 140
x(31-x) = 140
31x - x^2 - 140 = 0
x^2 - 31x + 140 = 0

x = (31 ± √401)/2
= appr 25.512.. or 5.4875..
then y = 5.4875 or 25.512

the two numbers are (31+√401)/2 and (31-√401)/2