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Katen [24]
3 years ago
11

Which two numbers add up to -24 and multiple to -24

Mathematics
1 answer:
Aleks [24]3 years ago
7 0
X + y = -24
xy = -24

xy = -24
\frac{xy}{x} = \frac{-24}{x}
y = \frac{-24}{x}

x + y = -24
x + \frac{-24}{x} = -24
\frac{x^{2}}{x} + \frac{-24}{x} = -24
\frac{x^{2} - 24}{x} = -24
-24x = x^{2} - 24
0 = x^{2} + 24x - 24
x = \frac{-(24) \± \sqrt{(24)^{2} - 4(1)(-24)}}{2(1)}
x = \frac{-24 \± \sqrt{576 + 96}}{2}
x = \frac{-24 \± \sqrt{672}}{2}
x = \frac{-24 \± 4\sqrt{42}}{2}
x = -12 \± 2\sqrt{42}
x = -12 \±  2(6.5)
x = -12 \± 13
x = -12 + 13    or    x = -12 - 13
x = 1    or    x = -25

  x + y = -24      or      x + y = -24
  1 + y = -24    or    -25 + y = -24
- 1           - 1         + 25        + 25
        y = -25        or         y = 1
  (x, y) = (1, -25)  or  (x, y) = (-25, 1)

The two numbers that add up to 24 are the numbers 1 and -25.

x + y = -24
xy = -24

xy = -24
\frac{xy}{x} = \frac{-24}{x}
y = \frac{-24}{x}

x + y = -24
x + \frac{-24}{x} = -24
\frac{x^{2}}{x} + \frac{-24}{x} = -24
\frac{x^{2} - 24}{x} = -24
-24x = x^{2} - 24
0 = x^{2} + 24x - 24
x = \frac{-(24) \± \sqrt{(24)^{2} - 4(1)(-24)}}{2(1)}
x = \frac{-24 \± \sqrt{576 + 96}}{2}
x = \frac{-24 \± \sqrt{672}}{2}
x = \frac{-24 \± 4\sqrt{42}}{2}
x = -12 \± 2\sqrt{42}
x = -12 \± 2(6)
x = -12 \± 12
x = -12 + 12    or    x = -12 - 12
x = 0    or    x = -24

  x + y = -24      or      x + y = -24
  0 + y = -24    or    -24 + y = -24
- 0           - 0         + 24        + 24
        y = 24         or         y = 0

The two numbers that multiply to -24 are the numbers 24 and 0.
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