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∵集合A={-1,1,3},B={a+2,a2+2},A∩B={3},∴當a+2=3時,a=1,B={3,3},不成立;當a2+2=3時,a=±1,當a=1時不成立,當a=-1時,B={1,3},A∩B={1,3},不成立.∴a的值不存在.故答案為:不存在.
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