  Within unitary transformed Hamiltonian of Fr\"ohlich type, using the Green's
functions method, exact renormalized energy spectrum of quasiparticle strongly
interacting with two-mode polarization phonons is obtained at $T=0$ K in a
model of the system with limited number of its initial states. Exact analytical
expressions for the average number of phonons in ground state and in all
satellite states of the system are presented. Their dependences on a magnitude
of interaction between quasiparticle and both phonon modes are analyzed.
