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vovangra [49]
3 years ago
11

What two numbers can be multiplied to be -150 and added to be 5

Mathematics
1 answer:
pav-90 [236]3 years ago
8 0
Xy = -150
x + y = 5

     x + y = 5
x - x + y = -x + 5
           y = -x + 5

                                                       xy = -150
                                             x(-x + 5) = -150
                                         x(-x) + x(5) = -150
                                               -x² + 5x = -150
                                     -x² + 5x + 150 = 0
                       -1(x²) - 1(-5x) - 1(-150) = 0
                                  -1(x² - 5x - 150) = 0
                                               -1            -1
                                        x² - 5x - 150 = 0
                                        x = -(-5) ± √((-5)² - 4(1)(-150))
                                                                2(1)
                                        x = 5 ± √(25 + 600)
                                                         2
                                        x = 5 ± √(625)
                                                     2
                                        x = 5 ± 25
                                                 2
                                        x = 2.5 ± 12.5
                                        x = 2.5 + 12.5    or    x = 2.5 - 12.5
                                        x = 15          or          x = -10

    x + y = 5
  15 + y = 5
- 15      - 15
          y = -10
    (x, y) = (15, -10)

            or

    x + y = 5
 -10 + y = 5
+ 10    + 10
           y = 15
    (x, y) = (-10, 15)

The two numbers that add up to 5 and multiply to -150 are 15 and -10.
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