Answer
A pair of concentric spheres.
Work Step by Step
Conversion of rectangular to spherical coordinates is as follows:
$x=\rho \sin \phi \cos \theta; y=\rho \sin \phi \sin \theta;z=\rho \cos \phi$
and
$\rho=\sqrt {x^2+y^2+z^2}$;
$\cos \phi =\dfrac{z}{\rho}$; $\cos \theta=\dfrac{x}{\rho \sin \phi}$
Here, $\rho^2-3\rho+2=0$
This implies that $(\rho-1)(\rho-2)=0$
or, $\rho=1,2$
Here, $\rho=1$ shows a sphere centered at the origin with radius $1$ and $\rho=2$ shows a sphere centered at the origin with radius $2$.
Hence, the given equation shows a pair of concentric spheres.
