Which two numbers add up to 20 in multiply to - 3

X + y = 20

xy = - 3

x + y = 20

x - x + y = - x + 20

y = - x + 20

xy = - 3

x (-x + 20) = - 3

x (-x) + x (20) = - 3

-x² + 20x = - 3

-x² + 20x + 3 = 0

-1 (x²) - 1 (-20x) - 1 (-3) = 0

-1 (x² - 20x - 3) = 0

-1 - 1

x² - 20x - 3 = 0

x = - (-20) ± √ ((-20) ² - 4 (1) (-3))

2 (1)

x = 20 ± √ (400 + 12)

2

x = 20 ± √ (412)

2

x = 20 ± 2√ (103)

2

x = 10 ± √ (103)

x = 10 + √ (103) or x = 10 - √ (103)

x + y = 20

10 + √ (103) + y = 20

- (10 + √ (103)) - (10 + √ (103))

y = 10 - √ (103)

(x, y) = (10 + √ (103), 10 - √ (103))

or

x + y = 20

10 - √ (103) + y = 20

- (10 - √ (103)) - (10 - √ (103))

y = 10 + √ (103)

(x, y) = (10 - √ (103), 10 + √ (103))

The two numbers that add up to 20 and multiply to - 3 are 10 ± √ (103).