若集合A={4,X²,2X-1,-4},B={x-5,1-x,9},若A∩B={9},求X
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![若集合A={4,X²,2X-1,-4},B={x-5,1-x,9},若A∩B={9},求X](/uploads/image/z/2590211-11-1.jpg?t=%E8%8B%A5%E9%9B%86%E5%90%88A%3D%7B4%2CX%26%23178%3B%2C2X-1%2C-4%7D%2CB%3D%7Bx-5%2C1-x%2C9%7D%2C%E8%8B%A5A%E2%88%A9B%3D%7B9%7D%2C%E6%B1%82X)
若集合A={4,X²,2X-1,-4},B={x-5,1-x,9},若A∩B={9},求X
若集合A={4,X²,2X-1,-4},B={x-5,1-x,9},若A∩B={9},求X
若集合A={4,X²,2X-1,-4},B={x-5,1-x,9},若A∩B={9},求X
若集合A={4,X²,2X-1,-4},B={x-5,1-x,9},若A∩B={9},则有
{x-5,1-x}∩{4,-4}=空集
(1)所以x≠9,x≠-1,x≠-3,x≠5
{X²,2X-1}∩{9}={9}
(2)所以x=3或x=-3或x=5
(3)由x-5≠1-x,X²≠2X-1得x≠3,x≠1
综合(1)、(2)、(3)得
x=5
而x=5时A∩B={-4,9}不符
x无解