Refer to Problems 1, 2, and 3. Show that the harmonic mean of a and b equals the geometric...

Refer to Problems 1, 2, and 3. Show that the harmonic mean of a and b equals the geometric mean squared divided by the arithmetic mean.

Problems 1

Arithmetic Mean If a < b, show that  The number  

is called the arithmetic mean of a and b.

Problems 2

Geometric Mean If 0 < a < b, show that  The number is called the geometric mean of a and b.

Problems 3

Harmonic Mean For 0<a < b, let h be defined by

Show that a < h < b. The number h is called the harmonic mean of a and b.