已知集合A={x丨4x²-11ax+8b=0}和B={x丨x²-ax+b=0},满足(补集A)∩B={2},A∩(补集B)={4},U=R,求实数a,b的值.
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![已知集合A={x丨4x²-11ax+8b=0}和B={x丨x²-ax+b=0},满足(补集A)∩B={2},A∩(补集B)={4},U=R,求实数a,b的值.](/uploads/image/z/7136055-63-5.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%EF%BD%9Bx%E4%B8%A84x%26%23178%3B-11ax%2B8b%3D0%EF%BD%9D%E5%92%8CB%3D%EF%BD%9Bx%E4%B8%A8x%26%23178%3B-ax%2Bb%3D0%EF%BD%9D%2C%E6%BB%A1%E8%B6%B3%EF%BC%88%E8%A1%A5%E9%9B%86A%EF%BC%89%E2%88%A9B%3D%EF%BD%9B2%EF%BD%9D%2CA%E2%88%A9%EF%BC%88%E8%A1%A5%E9%9B%86B%29%3D%EF%BD%9B4%EF%BD%9D%2CU%3DR%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%2Cb%E7%9A%84%E5%80%BC.)
已知集合A={x丨4x²-11ax+8b=0}和B={x丨x²-ax+b=0},满足(补集A)∩B={2},A∩(补集B)={4},U=R,求实数a,b的值.
已知集合A={x丨4x²-11ax+8b=0}和B={x丨x²-ax+b=0}
,满足(补集A)∩B={2},A∩(补集B)={4},U=R,求实数a,b的值.
已知集合A={x丨4x²-11ax+8b=0}和B={x丨x²-ax+b=0},满足(补集A)∩B={2},A∩(补集B)={4},U=R,求实数a,b的值.
由前一条件知x=2是B中方程的解,得4-2a+b=0;
由后一条件知x=4是A中方程的解,得16-44a+8b=0,即4-11a+2b=0,
解得a= -4/7,b= -36/7.