what multiplies to -1 and adds to 2

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lindseythornton lindseythornton

19-04-2016
Mathematics

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what multiplies to -1 and adds to 2

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Panoyin Panoyin · Answer 1 · 2016-04-19T23:08:07+02:00

  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).