On solutions of Bethe equations for the $XXZ$ model

It is shown that solutions of the Bethe ansatz equations for the inhomogeneous arbitrary spin $XXX$ or $XXZ$ model satisfy certain identites which generalize those, recently obtained by K. Fabricius and B. M. McCoy, for solutions of the Bethe ansatz equations for the six-vertex model. Even in the last case, the given proof is simpler than the original one.