If show that a, b, c, d are in G.P.

Given
      (a + bx) (b - cx) = (a - bx) (b + cx)
or      ab - acx + b²x - bcx² = ab + cax - b²x - bcx²
or               b²x + b²x  = cax + acx
                2b²x = 2acx      or        b² = ac   or                   ...(i)
Also,            
 
                              
or                                         or                            ...(ii)
From (i) and (ii), we have
                 
Hence, a, b, c are in G.P.