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AVprozaik [17]
3 years ago
9

What multiplies to -1 and adds to 2

Mathematics
1 answer:
jok3333 [9.3K]3 years ago
5 0
    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).
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