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.
