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By analyzing e+e− annihilation data corresponding to an integrated luminosity of 2.93fb−1 collected at the center-of-mass energy of 3.773\,GeV with the BESIII detector, we report the first observations of the doubly Cabibbo-suppressed decays D+→K+π0π0 and D+→K+π0η. The branching fractions of D+→K+π0π0 and D+→K+π0η are measured to be (2.1±0.4stat±0.1syst)×10−4 and (2.1±0.6stat±0.1syst)×10−4 with statistical significances of 8.0σ and 5.0σ, respectively. In addition, we search for the subprocesses D+→K∗(892)+π0 and D+→K∗(892)+η with K∗(892)+→K+π0. The branching fraction of D+→K∗(892)+η is determined to be (4.7+1.9−1.6stat±0.2syst)×10−4, with a statistical significance of 3.3σ. No significant signal for D+→K∗(892)+π0 is found and we set an upper limit on the branching fraction of this decay at the 90\% confidence level to be 4.5×10−4.