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Dmitriy789 [7]
3 years ago
11

What multiplies to -900 and adds to 5?

Mathematics
1 answer:
liq [111]3 years ago
6 0
Xy = -900
x + y = 5

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

                                                xy = -900
                                      x(-x + 5) = -900
                                  x(-x) + x(5) = -900
                                       -x² + 5x = -900
                             -x² + 5x + 900 = 0
               -1(x²) - 1(-5x) - 1(-900) = 0
                          -1(x² - 5x - 900) = 0
                                       -1            -1
                               x² - 5x - 900 = 0
                               x = -(-5) ± √((-5)² - 4(1)(-900))
                                                      2(1)
                               x = 5 ± √(25 + 3600)
                                                  2
                               x = 5 ± √(3625)
                                             2
                               x = 5 ± 5√(145)
                                           2
                               x = 2.5 ± 2.5√(145)

                          x + y = 5
   2.5 ± 2.5 √(145) + y = 5
- (2.5 ± 2.5√(145)       - (2.5 ± 2.5√(145)
                                y = 2.5 ± 2.5√(145)
                          (x, y) = (2.5 ± 2.5√(145), 2.5 ± 2.5√(145))

The two numbers that add up to 5 and multiply to -900 are 2.5 ± 2.5√(145).
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