1)

 

  and  are the roots of x² - 3x + a = 0. SO :  +  = 3   = a

 

  and  are the roots of x² - 12x + b = 0. SO :  +  = 12   = b

 

, , ,  are in G.P. Let  = p ;  = pq ;  = pq² ;  = pq³

 

ie, p + pq = p(1 + q) = 3 --------- (1)

     pq² + pq³ = pq²(1 + q) = 12 ---------- (2)

 

Solving (1) and (2) to get q = 2 and p = 1.

 

SO : a = p²q = 2                     &                         b = p²q⁵ = 32