If a, x, b are in H.P. and a, y, z, b are in G.P., then the value of yzxy3+z3 is

x=2aba+hLet common ratio of G.P. a, y, z, bbe r, then r3 = b/a andy=ar,z=b/r∴yz=aband y3+z3=a3r3+b3r3=a3ba+b3ab=ab(a+b)⇒xy3+z3=2aba+b(ab)(a+b)=2a2b2∴yzxy3+z3=ab2(ab)2=12ab