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TEA [102]
3 years ago
12

What two numbers add to 15 and multiply to negative 312?

Mathematics
1 answer:
natima [27]3 years ago
6 0
X + y = 15
xy = -312

     x + y = 15
x - x + y = -x + 15
           y = -x + 15

                                           xy = -312
                               x(-x + 15) = -312
                           x(-x) + x(15) = -312
                                 -x² + 15x = -312
                       -x² + 15x + 312 = 0
           -1(x²) - 1(-15x) - 1(312) = 0
                    -1(x² - 15x + 312) = 0
                                  -1              -1
                          x² - 15x + 312 = 0
                          x = -(-15) ± √((-15)² - 4(1)(312))
                                                  2(1)
                          x = 15 ± √(225 - 1248)
                                               2
                          x = 15 ± √(-1023)
                                         2
                          x = 15 ± 31.984i
                                         2
                          x = 7.5 ± 15.992
                          x = 7.5 + 15.992    or    x = 7.5 - 15.992
                          x = 23.492        or         x = -8.492

              x + y = 15
     23.492 + y = 15
   - 23.492        - 23.492
                    y = -8.492
              (x, y) = (23.492, -8.492)

                      or

              x + y = 15
     -8.492 + y = 15
   + 8.492         + 8.492
                   y = 23.492
             (x, y) = (-8.492, 23.492)

The two numbers that add up to 15 and mutliply to -312 are -8.492 and 23.492.
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