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Branching fraction and effective lifetime measurements of the rare decay B0s→μ+μ− and searches for the decays B0→μ+μ− and B0s→μ+μ−γ are reported using proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a luminosity of 9 fb−1. The branching fraction B(B0s→μ+μ−)=(3.09+0.46+0.15−0.43−0.11)×10−9 and the effective lifetime τ(B0s→μ+μ−)=2.07±0.29±0.03 ps are measured, where the first uncertainty is statistical and the second systematic. No significant signal for B0→μ+μ− and B0s→μ+μ−γ decays is found and upper limits B(B0→μ+μ−)