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:
