  We study theoretically a three-mode optomechanical system where two
mechanical oscillators are independently coupled to a single cavity mode. By
optimized two-tone or four-tone driving of the cavity one can prepare the
mechanical oscillators in an entangled two-mode squeezed state, even if they
start in a thermal state. The highly-pure, symmetric steady-state achieved
allows the optimal fidelity of standard continuous-variable teleportation
protocols to be achieved. In contrast to other reservoir engineering approaches
to generating mechanical entanglement, only a single reservoir is required to
prepare the highly-pure entangled steady-state, greatly simplifying
experimental implementation. The entanglement may be verified via a bound on
the Duan inequality obtained from the cavity output spectrum. A similar
technique may be used for the preparation of a highly-pure two-mode squeezed
state of two cavity modes, coupled to a common mechanical oscillator.
