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Within unitary transformed Hamiltonian of Fr\"ohlich type, using the Green'sfunctions method, exact renormalized energy spectrum of quasiparticle stronglyinteracting with two-mode polarization phonons is obtained at $T=0$ K in amodel of the system with limited number of its initial states. Exact analyticalexpressions for the average number of phonons in ground state and in allsatellite states of the system are presented. Their dependences on a magnitudeof interaction between quasiparticle and both phonon modes are analyzed.

Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at $T=0$ K