The correct option is C 2xyz
It is given that x is the arithmetic mean of y and z.
∴x=y+z2⇒2x=y+z
Since, G1 and G2 are two geometric means between y and z, so y, G1, G2, z are in a GP with common ratio r=(z/y)13.G1=yr⇒G31=y3r3=y3((zy)13)3=y2zG2=yr2⇒G32=y3r6=y3((zy)13)6=yz2
G31+G32=y2z+yz2=yz(y+z)=yz×2x=2xyz