Are there 2 numbers add to make 9 and multiply to make 4?

Answer 1

There are not two INTEGERS that can add to make 9 and multiply to make 4, however there are some Irrational Numbers that will do the job.

Let x and y be the two numbers.

x + y = 9

xy = 4 so y = 4/x

x + 4/x = 9

x² + 4 = 9x

x² - 9x + 4 = 0

using the quadratic formula,

x = (9 ± √[81-4(1)(4)])/2 = (9 ± √{81-16])/2 = (9 ±√65)/2

≈ 8.531129 or 0.468871

So the two numbers are approximately 0.468871 and 8.531129