若A={2,4,x的三次方-2x²-x-7}B={1,x+1,x²-2x+2,1/2(x²-3x-8),x三次方+x²+3x+7}若A∩B={2,5}求实数x的值
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![若A={2,4,x的三次方-2x²-x-7}B={1,x+1,x²-2x+2,1/2(x²-3x-8),x三次方+x²+3x+7}若A∩B={2,5}求实数x的值](/uploads/image/z/5372014-22-4.jpg?t=%E8%8B%A5A%3D%7B2%2C4%2Cx%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9-2x%26%23178%3B-x-7%7DB%3D%7B1%2Cx%2B1%2Cx%26%23178%3B-2x%2B2%2C1%2F2%EF%BC%88x%26%23178%3B-3x-8%29%2Cx%E4%B8%89%E6%AC%A1%E6%96%B9%2Bx%26%23178%3B%2B3x%2B7%7D%E8%8B%A5A%E2%88%A9B%3D%7B2%2C5%7D%E6%B1%82%E5%AE%9E%E6%95%B0x%E7%9A%84%E5%80%BC)
若A={2,4,x的三次方-2x²-x-7}B={1,x+1,x²-2x+2,1/2(x²-3x-8),x三次方+x²+3x+7}若A∩B={2,5}求实数x的值
若A={2,4,x的三次方-2x²-x-7}
B={1,x+1,x²-2x+2,1/2(x²-3x-8),x三次方+x²+3x+7}若A∩B={2,5}求实数x的值
若A={2,4,x的三次方-2x²-x-7}B={1,x+1,x²-2x+2,1/2(x²-3x-8),x三次方+x²+3x+7}若A∩B={2,5}求实数x的值
首先由A∩B={2,5}可知,A中必定含5,且x^3-2x²-x-7=5……(1)
B中一定含2,5,且不含4
假设x+1=2,则x=1. 代入得x^3-2x²-x-7不等于5,显然错误
假设x+1=5,则x=4. 代入得x^3-2x²-x-7=5,x²-2x+2=10,1/2(x²-3x-8)=-2,x三次方+x²+3x+7=131
刚好满足题意
所以x=4
原式=x^2(x^2-3x-28)=x^2(x-7)(x+4)