Question

what two numbers go into the product of 24 and the sum -11

Answer 1

Answer: The two numbers are 3 and 8

Step-by-step explanation:

Let the 2 numbers be x and y

x + y = 11 and xy = 24

We have to find x and y

equation 1-x + y = 11

equation 2-xy = 24 =>

x = 24/y dividing both sides of the equation by x.

Now substitute into equation one

24/y + y = 11 Solve for y. Multiply both sides of the equation by y

24 + y^2 = 11y Get everything on one side equal to 0

y^2 - 11y + 24 = 0 Subtracting 11y from both sides of the equation

(y - 8)(y - 3) = 0 By factoring

Therefore: y - 8 = 0 v y - 3 = 0

By the Zero Product Rule = y = 8 v y = 3

y ∈ {3, 8}

For y = 3, x + y = 11

= x + 3 = 11

x = 8

For y = 8, x + y = 11

= x + 8 = 11

x = 3

x ∈ {3, 8)

Checking:

8*3=24

8+3=11