Question

geometric mean
the number ___ such that $\frac{a}{x} = \frac{x}{b}$, where a, b, and
x are _____________ numbers.

Explanation:

The geometric mean of two numbers \(a\) and \(b\) is defined as the number \(x\) that forms a proportion \(\frac{a}{x} = \frac{x}{b}\). For this proportion to be valid (and for the geometric mean to be a real, positive value consistent with the definition), \(a\), \(b\), and \(x\) must be positive real numbers.

Answer:

The number \(x\) such that \(\frac{a}{x} = \frac{x}{b}\), where \(a\), \(b\), and \(x\) are positive real numbers.