Got the answer from Himanshus post,
Let a and b be the two positive nos,
Given,
x = (a + b) / 2 = AM ..(i)
a, y, z, b are in G.P
To find: (y3 + z3) / xyz
Let the common ratio be r,
Therefore,
y = ar;
z = ar2;
b = ar3;
Therefore r3 = b/a ..(ii)
y3 + z3 = a3r3 + a3r6 ..(iii)
Now, Substitute (ii) in (iii), we have,
y3 + z3 = a2b + ab2 = ab (a + b) ..(iv)
yz = (ar)(ar2) = a2r3 = ab (because b = ar3) ..(v)
Substituting the values of equation (i), (iv) and (v) in
(y3 + z3) / xyz
We have,
(y3 + z3) / xyz = ab (a + b) / ab (a + b) / 2
= 2
Is the answer right???