What two numbers added together equals 52 but multiplied together equals 420?

Answer 1

Let the two numbers be designated by p and q. From the statement of the problem,

pq = 420 and p + q = 52. From the second of these equations, p = 52 - q. Substituting this into the first equation yields (52 - q)q = 420, and expanding this equation yield 52 q -q2 = 420, or q2 - 56q + 420 = 0. This is equivalent to:

(q-42)(q-10) = 0, which is true when q = 10 or q = 42. Therefore, the two numbers are 42 and 10.