Question

What two numbers multiply to get -48 and add to get 2

Answer 1

xy = -48
x + y = 2


`xy = -48`

`(xy)/(x) = (-48)/(x)`

`y = (-48)/(x)`


`x + y = 2`

`x + (-48)/(x) = 2`

`(x^(2))/(x) + (-48)/(x) = 2`

`(x^(2) - 48)/(x) = 2`

`2x = x^(2) - 48`

`0 = x^(2) - 2x - 48`

`x = \frac{-(-2) \± \sqrt{(-2)^(2) - 4(1)(-48)}}{2(1)}`

`x = (2 \± √(4 + 192))/(2)`

`x = (2 \± √(196))/(2)`

`x = (2 \± 14)/(2)`

`x = (1 \± 7)/(1)`

`x =(1 + 7)/(1)`
`or`
`x = (1 - 7)/(1)`

`x = (8)/(1)`
`or`
`x = (-6)/(1)`

`x = 8`
`or`
`x = -6`

x + y = 2
8 + y = 2
- 8 - 8
y = -6
(x, y) = (8, -6)

x + y = 2
-6 + y = 2
+ 6 + 6
y = 8
(x, y) = (-6, 8)

The two numbers that multiply to -48 and add up to 2 are the numbers -6 and 8.