Question

Which two numbers add up to -24 and multiple to -24

Answer 1

x + y = -24
xy = -24


`xy = -24`

`(xy)/(x) = (-24)/(x)`

`y = (-24)/(x)`


`x + y = -24`

`x + (-24)/(x) = -24`

`(x^(2))/(x) + (-24)/(x) = -24`

`(x^(2) - 24)/(x) = -24`

`-24x = x^(2) - 24`

`0 = x^(2) + 24x - 24`

`x = \frac{-(24) \± \sqrt{(24)^(2) - 4(1)(-24)}}{2(1)}`

`x = (-24 \± √(576 + 96))/(2)`

`x = (-24 \± √(672))/(2)`

`x = (-24 \± 4√(42))/(2)`

`x = -12 \± 2√(42)`

`x = -12 \± 2(6.5)`

`x = -12 \± 13`

`x = -12 + 13`
`or`
`x = -12 - 13`

`x = 1`
`or`
`x = -25`

x + y = -24 or x + y = -24
1 + y = -24 or -25 + y = -24
- 1 - 1 + 25 + 25
y = -25 or y = 1
(x, y) = (1, -25) or (x, y) = (-25, 1)

The two numbers that add up to 24 are the numbers 1 and -25.

x + y = -24
xy = -24


`xy = -24`

`(xy)/(x) = (-24)/(x)`

`y = (-24)/(x)`


`x + y = -24`

`x + (-24)/(x) = -24`

`(x^(2))/(x) + (-24)/(x) = -24`

`(x^(2) - 24)/(x) = -24`

`-24x = x^(2) - 24`

`0 = x^(2) + 24x - 24`

`x = \frac{-(24) \± \sqrt{(24)^(2) - 4(1)(-24)}}{2(1)}`

`x = (-24 \± √(576 + 96))/(2)`

`x = (-24 \± √(672))/(2)`

`x = (-24 \± 4√(42))/(2)`

`x = -12 \± 2√(42)`

`x = -12 \± 2(6)`

`x = -12 \± 12`

`x = -12 + 12`
`or`
`x = -12 - 12`

`x = 0`
`or`
`x = -24`

x + y = -24 or x + y = -24
0 + y = -24 or -24 + y = -24
- 0 - 0 + 24 + 24
y = 24 or y = 0

The two numbers that multiply to -24 are the numbers 24 and 0.