If $x$ be the $A.M$ between $y$ and$z$... If $x$ be the AM between $y$ and $z$, $y$ be the GM between $z$ and $x$, then $x$, $y$, $z$ are in :
$1$). A.P
$2$). G.P
$3$). H.P
$4$). None.
My Attempt:
$x$ is the AM between $y$ and $z$
$$x=\dfrac {y+z}{2}$$
$$2x=y+z$$
$y$ is the G.M between $z$ and $x$.
$$y=\sqrt {zx}$$
$$y^2=xz$$
What should I do next?

HINT:
We have $$y+z=2x=2\cdot\dfrac{y^2}z\implies0=z^2+yz-2y^2=(z-y)(z+2y)$$
