若集合A={x丨x²-mx+m²-19=0},B={y丨y²-5y+6=0},C={z丨z²+2z-8=0},且A并B≠空集,A并C≠空集,求实数m的值
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![若集合A={x丨x²-mx+m²-19=0},B={y丨y²-5y+6=0},C={z丨z²+2z-8=0},且A并B≠空集,A并C≠空集,求实数m的值](/uploads/image/z/12077739-27-9.jpg?t=%E8%8B%A5%E9%9B%86%E5%90%88A%3D%EF%BD%9Bx%E4%B8%A8x%26%23178%3B-mx%2Bm%26%23178%3B-19%3D0%EF%BD%9D%2CB%3D%EF%BD%9By%E4%B8%A8y%26%23178%3B-5y%2B6%3D0%EF%BD%9D%2CC%3D%EF%BD%9Bz%E4%B8%A8z%26%23178%3B%2B2z-8%3D0%EF%BD%9D%2C%E4%B8%94A%E5%B9%B6B%E2%89%A0%E7%A9%BA%E9%9B%86%2CA%E5%B9%B6C%E2%89%A0%E7%A9%BA%E9%9B%86%2C%E6%B1%82%E5%AE%9E%E6%95%B0m%E7%9A%84%E5%80%BC)
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若集合A={x丨x²-mx+m²-19=0},B={y丨y²-5y+6=0},C={z丨z²+2z-8=0},且A并B≠空集,A并C≠空集,求实数m的值
若集合A={x丨x²-mx+m²-19=0},B={y丨y²-5y+6=0},C={z丨z²+2z-8=0},
且A并B≠空集,A并C≠空集,求实数m的值
若集合A={x丨x²-mx+m²-19=0},B={y丨y²-5y+6=0},C={z丨z²+2z-8=0},且A并B≠空集,A并C≠空集,求实数m的值
B={y丨y²-5y+6=0},B={y|(y-2)(y-3)=0},B={2,3}
C={z丨z²+2z-8=0},C={z|(z+4)(z-2)=0},C={-4,2}
A并B≠空集,得到:
4-2m+m²-19=0
9-3m+m²-19=0
分别解得:m=5或-3或2
A并C≠空集,得到:
16+4m+m²-19=0
4-2m+m²-19=0
分别解得:m=-2+根号7或-2-根号7或5或-3
两次运算所得m值的交集即m的值:5或-3