If 1 6 , and are in geometric progression, then the solution set of is

Step-by-step solution

Given that, terms 1 6 , and are in GP. aligned & ^2 = 1 6 & ^2 = ^2 6 & 6 ^3 - ^2 =0 & 6 ^3 -1+ ^2 =0 aligned aligned & 6 ^3 +1+ ^2 =0 & 6 ^3 + ^2 -1=0 & 6 ^3 +4 ^2 -3 ^2 +2 -2 -1=0 & 6 ^3 -3 ^2 +4 ^2 -2 +2 -1=0 & 3 ^2 (2 -1)+2 (2 -1)+1(2 -1) & =0 & (2 -1) (3 ^2 +2 +1 )=0 aligned For 3 ^2 +2 +1=0 value of will be imaginary so only 2 -1=0 will be considered to find . aligned & 2 -1=0 = 1 2 = 3 & =2 n 3 aligned