A search is performed for the charmless three-body decays of the Lambda(0)(b) and Xi(0)(b) baryons to the final states Lambda h(+)h(?-), where h()? = pi or K. The analysis is based on a data sample, corresponding to an integrated luminosity of 3 fb-1 of pp collisions, collected by the LHCb experiment. The Lambda(0)(b) -> Lambda K+pi(-) and Lambda(0)(b) -> Lambda K+K- decays are observed for the first time and their branching fractions and CP asymmetry parameters are measured. Evidence is seen for the Lambda(0)(b) -> Lambda pi(+)pi(-) decay and limits are set on the branching fractions of Xi(0)(b) baryon decays to the Lambda h(+)h(-) final states.
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