xy = 50
x + y = 6
\(xy = 50\)
\(\frac{xy}{x} = \frac{50}{x}\)
\(y = \frac{50}{x}\)
\(x + y = 6\)
\(x + \frac{50}{x} = 6\)
\(\frac{x^{2}}{x} + \frac{50}{x} = 6\)
\(\frac{x^{2} + 50}{x} = 6\)
\(x^{2} + 50 = 6x\)
\(x^{2} - 6x + 50 = 0\)
\(x = \frac{-(-6) \± \sqrt{(-6)^{2} - 4(1)(50)}}{2(1)}\)
\(x = \frac{6 \± \sqrt{36 - 100}}{2}\)
\(x = \frac{6 \± \sqrt{-64}}{2}\)
\(x = \frac{6 \± 8i}{2}\)
\(x = 3 \± 4i\)
\(x = 3 + 4i\) \(or\) \(x = 3 - 4i\)
x + y = 6
3 + 4i + y = 6
- (3 + 4i) - (3 + 4i)
y = 3 - 4i
(x, y) = (3 + 4i, 3 - 4i)
or
x + y = 6
3 - 4i + y = 6
- (3 - 4i) - (3 - 4i)
y = 3 + 4i
(x, y) = (3 - 4i, 3 + 4i)
(x, y) = (3 ± 4i, 3 ± 4i)
The two numbers that multiply to 50 and add up to 6 are 3 ± 4i.
