Permutations And Combinations

• Question

# If A and G are respectively the A.M. and G.M. between the two distinct positive numbers are a and b, then Prove A>G.

Solution

Since A is the A.M. between a and b

∴                 A =                                           ...(i)
Since G is the G.M. between a and b

∴                   G =                                          ...(ii)
A - G =

∴                          A - G > 0    A > G