Find two positive numbers whose difference is 12 and whose A.M. exceeds the GM. by 2.

Let a and b be two positive numbers such that
                              a - b = 12                                                                                                  ...(i)
Since  A.M. exceeds G.M. by 2

∴                                a + b =
                             
                                                                                                               ...(ii)
From (i),                         ...(iii)
Adding (ii) and (iii), we get    
Subtracting (ii) from (iii), we get