Try this Arithmetic Mean – Geometric Mean Subjective Problem number 82 from TOMATO.

* Problem*: Arithmetic Mean – Geometric Mean

Let be positive real numbers such that . Show that,

* Solution*:

=

[ AM-GM ]

= 4

=

[ AM-GM ]

= 6

=

[ AM-GM ]

= 4

Now, L.H.S =

=

= 16

= RHS. [ proved ]