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Galina-37 [17]
3 years ago
15

What two numbers multiply to 54 and add up to 7

Mathematics
1 answer:
k0ka [10]3 years ago
5 0
Xy = 54
x + y = 7

xy = 54
\frac{xy}{x} = \frac{54}{x}
y = \frac{54}{x}

x + y = 7
x + \frac{54}{x} = 7
\frac{x^{2}}{x} + \frac{54}{x} = 7
\frac{x^{2} + 54}{x} = 7
x^{2} + 54 = 7x
x^{2} - 7x + 54 = 0
x = \frac{-(-7) \± \sqrt{(-7)^{2} - 4(1)(54)}}{2(1)}
x = \frac{7 \± \sqrt{49 - 216}}{2}
x = \frac{7 \± \sqrt{-167}}{2}
x = \frac{7 \± i\sqrt{167}}{2}
x = \frac{7 \± 12.9i}{2}
x = 3.5 \± 6.45i
x = 3.5 + 6.45i    or    3.5 - 6.45i

                  x + y = 7
   3.5 + 6.45i + y = 7
- (3.5 + 6.45i)       - (3.5 + 6.45i)
                        y = 3.5 - 6.45i
                  (x, y) = (3.5 + 6.45i, (3.5 - 6.45i)

                          or

                  x + y = 7
   3.5 - 6.45i + y = 7
- (3.5 - 6.45i)     - (3.5 - 6.45i)
                       y = 3.5 + 6.45i
                 (x, y) = (3.5 - 6.45i, 3.5 + 6.45i)

The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.
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