x + y = 5
xy = 12
x + y = 5
y = -x + 5
xy = 12
x(-x + 5) = 12
x(-x) + x(5) = 12
-x² + 5x = 12
- 12 - 12
-x² + 5x - 12 = 0
x² - 5x + 12 = 0
x = 5 ± √25 - 48
2
x = -5 ± √-23
2
x = -5 ± 4.79i
2
x = -5 + 4.79i or x = -5 - 4.79i
2 2
x = -2.5 + 2.395i or x = -2.5 - 2.395i
y = -2.5 - 2.395i or y = -2.5 + 2.395i
The two numbers that add up to 5 and multiply to 12 is -2.5 ± 2.395i, which is -2.5 + 2.395i and -2.5 - 2.395i.
