已知集合A={x/x^2-ax+a^2-19=0},B={x/log2^(x^2-5x+8)=1},C=x/2^x^2+2x-x=1},A∩B≠空集和A∩C=空集,求实数a的值及集合A
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![已知集合A={x/x^2-ax+a^2-19=0},B={x/log2^(x^2-5x+8)=1},C=x/2^x^2+2x-x=1},A∩B≠空集和A∩C=空集,求实数a的值及集合A](/uploads/image/z/1030568-32-8.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7Bx%2Fx%5E2-ax%2Ba%5E2-19%3D0%7D%2CB%3D%7Bx%2Flog2%5E%28x%5E2-5x%2B8%29%3D1%7D%2CC%3Dx%2F2%5Ex%5E2%2B2x-x%3D1%7D%2CA%E2%88%A9B%E2%89%A0%E7%A9%BA%E9%9B%86%E5%92%8CA%E2%88%A9C%3D%E7%A9%BA%E9%9B%86%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC%E5%8F%8A%E9%9B%86%E5%90%88A)
已知集合A={x/x^2-ax+a^2-19=0},B={x/log2^(x^2-5x+8)=1},C=x/2^x^2+2x-x=1},A∩B≠空集和A∩C=空集,求实数a的值及集合A
已知集合A={x/x^2-ax+a^2-19=0},B={x/log2^(x^2-5x+8)=1},C=x/2^x^2+2x-x=1},
A∩B≠空集和A∩C=空集,求实数a的值及集合A
已知集合A={x/x^2-ax+a^2-19=0},B={x/log2^(x^2-5x+8)=1},C=x/2^x^2+2x-x=1},A∩B≠空集和A∩C=空集,求实数a的值及集合A
因为log2^(x^2-5x+8)=1=log2^2,所以x^2-5x+8=2,可解得x=2或3
2^x^2+2x-x=1,可解得x=0
又因为A∩B≠空集,所以:
当x=2时,4-2a+a^2-19=0,可解a=5或-3
当x=3时,9-3a+a^2-19=0,所以a=5或-2
综上所述,a=5、-2、-3,A={2},A={3},A={2,3},