Let x be the arithmetic mean and y, z be the two geometric means between any two positive numbers.Then value of y3+z3xyz is

Let two positive numbers be a and b. Then x=(a+b)/2. Also,  a, y, z, b are in G.P.If r is the common ratio of this G.P…, then b=ar3⇒r=(b/a)1/3.We have y3+z3xyz=a3r3+a3r6x(ar)ar2=a1+r3x=a+b(a+b)/2=2