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).
