Question

Find two numbers whose product is 80 and whose sum is 18

Answer 1

Let X & Y be the two integers

X+Y=18      Y = 18-X

XY = 80

We can substitute 18-X for Y in the equation XY = 80

X(18-X) = 80

Distributing

18X - X2 = 80

Subtract 80 from both sides so that the equation is equal to 0

-X2 + 18X - 80 = 0

Multiply (or divide by -1 so that the leading coefficient is positive, not negative)

X2 - 18X + 80 = 0

We can factor this quadratic

(X-10)(X-8) = 0

Setting each factor equal to 0 we can solve for X.

X-10 = 0       X-8 = 0

X = 10          X = 8

The two integers are 8 and 10.Answer:

Step-by-step explanation: