Question

Find HM of two positive number where AM and GM are 16 and 18 respectively.

Answer 1

$AM=16\frac{a+b}{2}=16a+b=32GM=18\sqrt{ab}=18ab=324$

$HM$ of $2$ no's

${\left(\frac{\frac{1}{a}+\frac{1}{b}}{2}\right)}^{-1}={\left(\frac{a+b}{2ab}\right)}^{-1}=\frac{2ab}{a+b}=\frac{2\times 324}{32}=20.25$