集合A={x|x²-ax+a²-19=0},B={x|x²-5x+6=0},C={x|x²+2x-8=0}满足A‿B=φ,A‿C不等于空集,A并b等于空集,求实数a的值
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![集合A={x|x²-ax+a²-19=0},B={x|x²-5x+6=0},C={x|x²+2x-8=0}满足A‿B=φ,A‿C不等于空集,A并b等于空集,求实数a的值](/uploads/image/z/805175-71-5.jpg?t=%E9%9B%86%E5%90%88A%3D%EF%BD%9Bx%EF%BD%9Cx%26%23178%3B%EF%BC%8Dax%2Ba%26%23178%3B%EF%BC%8D19%3D0%EF%BD%9D%2CB%3D%EF%BD%9Bx%EF%BD%9Cx%26%23178%3B%EF%BC%8D5x%2B6%3D0%EF%BD%9D%2CC%3D%EF%BD%9Bx%EF%BD%9Cx%26%23178%3B%2B2x%EF%BC%8D8%3D0%EF%BD%9D%E6%BB%A1%E8%B6%B3A%26%238255%3BB%3D%CF%86%2CA%26%238255%3BC%E4%B8%8D%E7%AD%89%E4%BA%8E%E7%A9%BA%E9%9B%86%2CA%E5%B9%B6b%E7%AD%89%E4%BA%8E%E7%A9%BA%E9%9B%86%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC)
集合A={x|x²-ax+a²-19=0},B={x|x²-5x+6=0},C={x|x²+2x-8=0}满足A‿B=φ,A‿C不等于空集,A并b等于空集,求实数a的值
集合A={x|x²-ax+a²-19=0},B={x|x²-5x+6=0},C={x|x²+2x-8=0}满足A‿B=φ,A‿C不等于空集,A并b等于空集,求实数a的值
集合A={x|x²-ax+a²-19=0},B={x|x²-5x+6=0},C={x|x²+2x-8=0}满足A‿B=φ,A‿C不等于空集,A并b等于空集,求实数a的值
B:x²-5x+6=0,(x-2)(x-3)=0,x=2,x=3
C:x²+2x-8=0,(x+4)(x-2)=0,x=2,x=-4
A:x²-ax+a²-19=0,x=-4,x≠2
则 16+4a+a^2-19=0,a^2+4a-3=0,(a+2)^2-7=0
(a+2+√7)(a+2-√7)=0
a=-2-√7
a=-2+√7
【验证
x=2,4-2a+a^2-19=0,a^2-2a-15=0,(a-5)(a+3)=0,a=5,a=-3
∴
a=-2-√7
a=-2+√7
A∪B是空集,说明他俩联合起来无解。
所以,(a+5)x +13- a² =0无解
所以 a= - 5
经友人提醒,我做错了……不要看我的……