  We use the zero-range approximation to study a system of two identical bosons
interacting resonantly with a third particle. The method is derived from
effective field theory. It reduces the three-body problem to an integral
equation which we then solve numerically. We also develop an alternative
approach which gives analytic solutions of the integral equation in coordinate
representation in the limit of vanishing total energy. The atom-dimer
scattering length, the rates of atom-dimer relaxation and three-body
recombination to shallow and to deep molecular states are calculated either
analytically or numerically with a well controlled accuracy for various
energies as functions of the mass ratio, scattering length, and three-body
parameter. We discuss in detail the relative positions of the recombination
loss peaks, which in the universal limit depend only on the mass ratio. Our
results have implications for ongoing and future experiments on Bose-Bose and
Bose-Fermi atomic mixtures.
