Question

Which numbers multiply to 50 and add to 6

Answer 1

xy = 50
x + y = 6


`xy = 50`

`(xy)/(x) = (50)/(x)`

`y = (50)/(x)`


`x + y = 6`

`x + (50)/(x) = 6`

`(x^(2))/(x) + (50)/(x) = 6`

`(x^(2) + 50)/(x) = 6`

`x^(2) + 50 = 6x`

`x^(2) - 6x + 50 = 0`

`x = \frac{-(-6) \± \sqrt{(-6)^(2) - 4(1)(50)}}{2(1)}`

`x = (6 \± √(36 - 100))/(2)`

`x = (6 \± √(-64))/(2)`

`x = (6 \± 8i)/(2)`

`x = 3 \± 4i`

`x = 3 + 4i`
`or`
`x = 3 - 4i`

x + y = 6
3 + 4i + y = 6
- (3 + 4i) - (3 + 4i)
y = 3 - 4i
(x, y) = (3 + 4i, 3 - 4i)

or
x + y = 6
3 - 4i + y = 6
- (3 - 4i) - (3 - 4i)
y = 3 + 4i
(x, y) = (3 - 4i, 3 + 4i)

(x, y) = (3 ± 4i, 3 ± 4i)

The two numbers that multiply to 50 and add up to 6 are 3 ± 4i.