已知集合A={(x,y)|(y-3)/(x-2) .已知集合A={(x,y)∣(y-3)/(x-2)=a+1},B={(x,y)∣(a^2-1)x+(a-1)y-15=0},若A∩B=Φ,当a取何值时,A∩B=Φ.
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![已知集合A={(x,y)|(y-3)/(x-2) .已知集合A={(x,y)∣(y-3)/(x-2)=a+1},B={(x,y)∣(a^2-1)x+(a-1)y-15=0},若A∩B=Φ,当a取何值时,A∩B=Φ.](/uploads/image/z/8735900-68-0.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7B%EF%BC%88x%2Cy%29%7C%28y-3%29%2F%28x-2%29+.%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7B%28x%2Cy%29%E2%88%A3%28y-3%29%2F%28x-2%29%3Da%2B1%7D%2CB%3D%7B%28x%2Cy%29%E2%88%A3%28a%5E2-1%29x%2B%28a-1%29y-15%3D0%7D%2C%E8%8B%A5A%E2%88%A9B%3D%CE%A6%2C%E5%BD%93a%E5%8F%96%E4%BD%95%E5%80%BC%E6%97%B6%2CA%E2%88%A9B%3D%CE%A6.)
已知集合A={(x,y)|(y-3)/(x-2) .已知集合A={(x,y)∣(y-3)/(x-2)=a+1},B={(x,y)∣(a^2-1)x+(a-1)y-15=0},若A∩B=Φ,当a取何值时,A∩B=Φ.
已知集合A={(x,y)|(y-3)/(x-2) .
已知集合A={(x,y)∣(y-3)/(x-2)=a+1},B={(x,y)∣(a^2-1)x+(a-1)y-15=0},若A∩B=Φ,当a取何值时,A∩B=Φ.
已知集合A={(x,y)|(y-3)/(x-2) .已知集合A={(x,y)∣(y-3)/(x-2)=a+1},B={(x,y)∣(a^2-1)x+(a-1)y-15=0},若A∩B=Φ,当a取何值时,A∩B=Φ.
分析,集合A={(x,y)∣(y-3)/(x-2)=a+1}和集合B={(x,y)∣(a^2-1)x+(a-1)y-15=0}各位一条直线上的点,则A、B两条直线平行时,A∩B=Φ.还有,注意空集交任何集合是空集
一般两种解法:
1.A∩B=Φ,即方程组
(y-3)/(x-2)=a+1
(a^2-1)x+(a-1)y-15=0 无解 算吧……麻烦
2.分类讨论A∩B=Φ,
1) A,B都不为空集,直线(y-3)/(x-2)=a+1与直线(a^2-1)x+(a-1)y-15=0平行
斜率相等,得-(a^2-1)/(a-1)=a+1 解得a=-1
a=-1时,两条直线分别为y=3和y=-15/2,不重合
则a=-1时,A∩B=Φ
2)A为空集时,因为(2,3)不∈A,所以当(2,3)∈B时,A∩B=φ,代入B中解得
此时a=5/2或-4.
3)B为空集时,此时,a=1
因此当a=1,-1,5/2,-4时,A∩B=Φ