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Mathematics
Azul Guerrero
2 February, 12:55
Which two numbers add up to 20 in multiply to - 3
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Murphy
2 February, 13:40
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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).
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