x + y = 8
xy = 40
x + y = 8
x - x + y = -x + 8
y = -x + 8
xy = 40
x(-x + 8) = 40
x(-x) + x(8) = 40
-x² + 8x = 40
-x² + 8x - 40 = 0
-1(x²) - 1(-8x) - 1(40) = 0
-1(x² - 8x + 40) = 0
-1 -1
x² - 8x + 40 = 0
x = -(-8) ± √((-8)² - 4(1)(40))
2(1)
x = 8 ± √(64 - 160)
2
x = 8 ± √(-96)
2
x = 8 ± 4i√(6)
2
x = 4 + 2i√(6)
x = 4 + 2i√(6) or x = 4 - 2i√(6)
x + y = 8
4 ± 2i + y = 8
- (4 ± 2i) - (4 ± 2i)
y = 4 ± 2i
(x, y) = (4 ± 2i, 4 ± 2i)
The two numbers that add up to 8 and multiply to 40 are 4 ± 2i.