let a and b be two numbers
Then AM of aand b is given by \[\frac{a+b}{2} \] ....................................................(1)
Geometric mean is given by \[\sqrt{ab} \] .........................................................(2)
Harmonic mean is given by \[\frac{2ab}{a+b} \] .................................................................(3)
Multiplying equation 1 and 2 \[\left (\frac{a+b}{2} \right ) \times \left (\frac{2ab}{a+b} \right )= \left (ab \right)^{2} \] whic is equal to \[ G^2 \]
Hence \[ G = \sqrt[]{AH } \]
