What multiplies to - 1 and adds to 2

xy = - 1

x + y = 2

x + y = - 2

- x - x

y = - x - 2

xy = - 1

x (-x + 2) = - 1

x (-x) + x (2) = - 1

-x² + 2x = - 1

+ 1 + 1

-x² + 2x + 1 = 0

-1 (x²) - 1 (-2x) - 1 (-1) = 0

-1 (x² - 2x - 1) = 0

-1 - 1

x² - 2x - 1 = 0

x = - (-2) ± √ ((-2) ² - 4 (1) (-1))

2 (1)

x = 2 ± √ (4 - 4 (-1))

2

x = 2 ± √ (4 + 4)

2

x = 2 ± √ (8)

2

x = 2 ± 2√ (2)

2

x = 1 ± √ (2)

x + y = 2

(1 ± √ (2)) + y = 2

- (1 ± √ (2)) - (1 ± √ (2))

y = 1 ± √ (2)

(x, y) = (1 ± √ (2), 1 ± √ (2))

The numbers that multiply to - 1 and add to 2 are 1 ± √ (2).