Extended Inequality Satisfied by Pythagorean Classical Means

The great mathematician Pythagoras who is the inventor of the three basic measures of average namely Arithmetic Mean, Geometric Mean & Harmonic Mean, which are termed as the Pythagorean classical means, derived an inequality satisfied by these three measures in a domain of numbers. An inequality has here been derived which is satisfied by the three Pythagorean classical means in a wider domain of numbers. This article presents the derivation of this extended inequality with numerical example.