Question

What two numbers multiply to get 54 and add to get 36?

Answer 1

Let the numbers be x and y.
given that their sum, x+y = 36
⇒ y = 36-x

product = xy = 54
⇒ x( 36 - x) = 54
⇒ 36x - x² = 54
⇒ x² - 36x +54 = 0

Solving the quadratic equation, we get
x = 18 + 3√30 and 18-3√30

So the numbers are 18 + 3√30 and 18-3√30