  We present VLT near-IR spectroscopic observations of three X-ray sources
characterized by extremely high X-ray-to-optical ratios (X/O>40), extremely red
colors (6.3<R-K<7.4, i.e. EROs) and bright infrared magnitudes (17.6<K<18.3).
These objects are very faint in the optical, making their spectroscopic
identification extremely challenging. Instead, our near-IR spectroscopic
observations have been successful in identifying the redshift of two of them
(z=2.08 and z=1.35), and tentatively even of the third one (z=2.13). When
combined with the X-ray properties, our results clearly indicate that all these
objects host obscured QSOs (4e44 < L(2-10keV) < 1.5e45 erg/s, 2e22 < N_H < 4e23
cm-2) at high redshift. The only object with unresolved morphology in the K
band shows broad Halpha emission, but not broad Hbeta, implying a type 1.9 AGN
classification. The other two objects are resolved and dominated by the host
galaxy light in the K band, and appear relatively quiescent: one of them has a
LINER-like emission line spectrum and the other presents only a single, weak
emission line which we tentatively identify with Halpha. The galaxy
luminosities for the latter two objects are an order of magnitude brighter than
typical local L* galaxies and the derived stellar masses are well in excess of
10^11 Msun. For these objects we estimate black hole masses higher than 10^9
Msun and we infer that they are radiating at Eddington ratios L/L_Edd < 0.1. We
discuss the implications of these findings for the coevolution of galaxies and
black hole growth. Our results provide further support that X-ray sources with
high X/O ratios and very red colors tend to host obscured QSO in very massive
galaxies at high redshift.
