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填空题
已知集合A＝{a2，a＋1，－3}，B＝{a－3，2a－1，a2＋1}，若A∩B＝{－3}，则实数a的值为____．
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参考解析
解析：
∵A∩B＝{－3}，∴－3∈B
∵ a2＋1＞0
∴集合B中元素有a－3＝－3，或2a－1＝－3．
当a－3＝－3，即a＝0时，A＝{0，1，－3}，B＝{－3，－1，1}，得A∩B＝{1，－3}，与已知A∩B＝{－3}相矛盾，故舍去a＝0；
当2a－1＝－3，即a＝－1时，A＝{1，0，－3}，B＝{－4，－3，2}，A∩B＝{－3}符合题意．
∴a＝－1
∵ a2＋1＞0
∴集合B中元素有a－3＝－3，或2a－1＝－3．
当a－3＝－3，即a＝0时，A＝{0，1，－3}，B＝{－3，－1，1}，得A∩B＝{1，－3}，与已知A∩B＝{－3}相矛盾，故舍去a＝0；
当2a－1＝－3，即a＝－1时，A＝{1，0，－3}，B＝{－4，－3，2}，A∩B＝{－3}符合题意．
∴a＝－1
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