已知集合A={a2,a+1,-3},B={a-3,2a-1,a2+1},若A∩B={-3},则a的值为( )
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已知集合A={a2,a+1,-3},B={a-3,2a-1,a2+1},若A∩B={-3},则a的值为( )
A. a=0或-1
B. a=0
C. a=-1
D. a=-2或0
A. a=0或-1
B. a=0
C. a=-1
D. a=-2或0
![已知集合A={a2,a+1,-3},B={a-3,2a-1,a2+1},若A∩B={-3},则a的值为( )](/uploads/image/z/4874515-43-5.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7Ba2%EF%BC%8Ca%2B1%EF%BC%8C-3%7D%EF%BC%8CB%3D%7Ba-3%EF%BC%8C2a-1%EF%BC%8Ca2%2B1%7D%EF%BC%8C%E8%8B%A5A%E2%88%A9B%3D%7B-3%7D%EF%BC%8C%E5%88%99a%E7%9A%84%E5%80%BC%E4%B8%BA%EF%BC%88%E3%80%80%E3%80%80%EF%BC%89)
∵A={a2,a+1,-3},B={a-3,2a-1,a2+1},若A∩B={-3},
∴a-3=-3或2a-1=-3或a2+1=-3,
解得:a=0或a=-1,
将a=0代入得:A={0,1,-3},B={-3,-1,1},此时A∩B={1,-3},不合题意;
将a=-1代入得:A={1,0,-3},B={-4,-3,2},此时A∩B={-3},满足题意,
则a=-1.
故选:B.
∴a-3=-3或2a-1=-3或a2+1=-3,
解得:a=0或a=-1,
将a=0代入得:A={0,1,-3},B={-3,-1,1},此时A∩B={1,-3},不合题意;
将a=-1代入得:A={1,0,-3},B={-4,-3,2},此时A∩B={-3},满足题意,
则a=-1.
故选:B.
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