[MATH]\phi^2 - \phi = 1[/MATH] (same as [MATH]\phi^2 = \phi + 1[/MATH]) \(\displaystyle \ \ \ \) <---- This equation has two solutions.[MATH]\left(\phi - \frac{1}{2}\right)^2 = 1 + \frac{1}{4}[/MATH][MATH]\phi - \frac{1}{2} = \sqrt{\frac{5}{4}}[/MATH][MATH]\phi = \frac{1}{2} + \frac{1}{2}\sqrt{5}[/MATH][MATH]\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618[/MATH]
There is but one golden ratio.<---- This equation has two solutions.