two numbers that add to 15 and multiply to 5

Question

I need help with this problem 

Answer 1

Here's what we know:

x + y = 15

x * y = 5

 

Isolate a variable for substitution:

x = 15 - y

y(15 - y) = 5

Factor:

15y - y² = 5

Create a quadratic equation:

-y² + 15y - 5 = 0

y² - 15y + 5 = 0

 

Since the equation isn't going to factor evenly, we can go to the Quadratic formula to find x and y:

(-b ± √(b² - 4ac)) / 2a

(-(-15) ± √((-15)² - 4*1*5)) / 2*1

(15 ± √(225 - 20)) / 2

(15 ± √205) / 2

 

x = (15 + √205) / 2

y = (15 - √205) / 2

Answer 2

x and y are the numbers

x+y=15

xy=5

x+y=15 means y=15-x

substitute

x(15-x)=5

15x-x^2=5

x^2-15x+5=0

using the quadratic equation I came up with:

(15-√205)/2 and (15+√205)/2