Means and the AM-GM inequality

Build tools for the two means, and use them to check the AM-GM inequality on many pairs.

The idea. $A = \dfrac{a + b}{2}$ and $G = \sqrt{ab}$, with $A \ge G$. $n$ geometric means between $a$ and $b$ have ratio $\left(\dfrac{b}{a}\right)^{\frac{1}{n + 1}}$. Two numbers with means $A$ and $G$ are $A \pm \sqrt{A^2 - G^2}$.

Your tasks.

1. In means, return the pair (A, G) for two positive numbers.
2. In insert_gms, return a list of the n geometric means between a and b.
3. In from_means, return the two numbers, larger first, whose means are A and G.