Аннотация:A search for the rare decays View the MathML source and B0→π+π−μ+μ− is performed in a data set corresponding to an integrated luminosity of 3.0 fb−1 collected by the LHCb detector in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV. Decay candidates with pion pairs that have invariant mass in the range 0.5–1.3 GeV/c2 and with muon pairs that do not originate from a resonance are considered. The first observation of the decay View the MathML source and the first evidence of the decay B0→π+π−μ+μ− are obtained and the branching fractions, restricted to the dipion-mass range considered, are measured to be View the MathML source and View the MathML source, where the third uncertainty is due to the branching fraction of the decay B0→J/ψ(→μ+μ−)K⁎(892)0(→K+π−), used as a normalisation.