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The production of the $K^*(892)$ strange resonance in Pb+Pb collisions at$\sqrt{s_{NN}}=2.76$ TeV LHC energy is analyzed within the integratedhydrokinetic model (iHKM) at different equations of state of superdense matter.The similar analysis is done also for the RHIC top energy $\sqrt{s_{NN}}=200$GeV for comparison purposes. A modification of experimental$K^*(892)$-identification is studied for different centralities in view ofpossible re-scattering of the decay products at the afterburner stage of thefireball evolution. We see quite intensive rescattering of the decay productsas well as recombination processes for $K^*(892)$. In addition, the productionof the much longer-long-lived $\phi(1020)$ resonance with hidden strange quarkcontent is investigated.

$K^*(892)$ and $\phi(1020)$ production and their decay into the hadronic medium at the Large Hadron Collider