What is the geometric mean of the golden ratio $\phi$ and ($\phi-1$) ?
A) 1
B) $\phi$
C) $\phi-1$
D) $\phi^{2}$

Question

Quizplus · Accepted Answer

The geometric mean of two numbers $a$ and $b$ is $\sqrt{ab}$. The golden ratio $\phi$ satisfies $\phi = 1 + \frac{1}{\phi}$, so $\phi - 1 = \frac{1}{\phi}$. Thus, the geometric mean of $\phi$ and $\phi - 1$ is $\sqrt{\phi(\phi - 1)} = \sqrt{\phi \cdot \frac{1}{\phi}} = \sqrt{1} = 1$.

What Is the Geometric Mean of the Golden Ratio ϕ\phiϕ And

What Is the Geometric Mean of the Golden Ratio $\phi$ And