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Neporo4naja [7]
3 years ago
5

What two numbers add up to 39 and multiply to -880?

Mathematics
1 answer:
Papessa [141]3 years ago
5 0
X + y = 39
xy = -880

     x + y = 39
x - x + y = -x + 39
           y = -x + 39

                                        xy = -880
                            x(-x + 39) = -880
                        x(-x) + x(39) = -880
                             -x² + 39x = -880
                   -x² + 39x + 880 = 0
     -1(x²) - 1(-39x) - 1(-880) = 0
                -1(x² - 39x - 880) = 0
                              -1             -1
                      x² - 39x - 880 = 0
            x² - 55x + 16x - 880 = 0
x(x) - x(55) + 16(x) - 16(55) = 0
           x(x - 55) + 16(x - 55) = 0
                    (x + 16)(x - 55) = 0
x + 16 = 0        or        x - 55 = 0
    - 16 - 16                    + 55 + 55
        x = -16          or          x = 55

      x + y = 39
  -16 + y = 39
+ 16       + 16
          y = 55
    (x, y) = (-16, 55)

           or

     x + y = 39
   55 + y = 39
 - 55        - 55
           y = -16
     (x, y) = (55, -16)

The two numbers that add up to 39 and multiply to -880 are 55 and -16.
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