Question

设集合A={x|(x-3)(x-a)小于等于0,a∈R},B={x|(x-4)(x-1)≤0},求A∪B,A∩B

Answer 1

这个题先求B={x|1<=x<=4}
这个题先求B解A的二次不等式
得x1=3，x2=a
若a>3,则A={x|3<=x<=a}，若a<=4,则A∪B={x|1<=x<=4}，A∩B={x|3<=x<=a}；
若a>=4,则A∪B={x|1<=x<=a}，A∩B={x|3<=x<=4}
若a=3,则A={3}，此时A∪B={x|1<=x<=4}，A∩B={x|1<=x<=4}
若a<3,则A={x|a<=x<=3}，若a<=1,则A∪B={x|a<=x<=4}，A∩B={x|1<=x<=3}；
若a>=1,则A∪B={x|1<=x<=4}，A∩B={x|a<=x<=3}