If ₆ a+ ₆ b+ ₆ c=6 , where a, b and c are positive integers that form an increasing GP and b-a is a square of an integer, then a+b+c=

Step-by-step solution

We have, ₆ a b c=6 a b c=6⁶...(i) Let b=a r, c=a r² Eq. (i), a³ r³=6⁶ b-x^ n =36b-a=36-a is square for a=35,32,27,20,11 array ll & c= b² a = 36² a is an integer for a=27 & a=27, b=36, c=48 & a+b+c=111 array