Which 2 numbers add up to 8, but multiply to get 40?

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.