Question 487743
Let a and b be two numbers with


*[tex \LARGE \frac{a+b}{2} = 5 \Rightarrow a+b = 10], and


*[tex \LARGE \frac{2}{\frac{1}{a} + \frac{1}{b}} = 3.2]


The second equation becomes


*[tex \LARGE \frac{2}{\frac{a+b}{ab}} = 3.2]


*[tex \LARGE \frac{2ab}{a+b} = 3.2], replace a+b with 10 to get


*[tex \LARGE \frac{2ab}{a+b} = \frac{2ab}{10} = 32 \Rightarrow ab = 16]


The geometric mean of a and b is *[tex \LARGE \sqrt{ab}], or *[tex \LARGE \sqrt{16} = 4].