A={x/2a≤x≤a+3}.B={x/x<-1或x>5}.求:①若A∩B≠空集,求a的取值范围.②若A∪B=R(R为实数集)

A={x/2a≤x≤a+3}.B={x/x<-1或x>5}.求:①若A∩B≠空集,求a的取值范围.②若A∪B=R(R为实数集),求a的取值范围.最好要有解题过程... A={x/2a≤x≤a+3}.B={x/x<-1或x>5}.求:①若A∩B≠空集,求a的取值范围.②若A∪B=R(R为实数集),求a的取值范围.最好要有解题过程 展开
雨天关门
2011-07-20 · TA获得超过189个赞
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1.画数轴,只要A有一部分在B上就是A∩B≠空集
∴A≠空集
∴2a≤a+3 又∵2a=a+3即a=3,A=3,不符合题意(舍去)
∴2a<a+3即a<3
①当2a<-1时A∩B≠空集即a<-1
②当2a≥-1时要使得A∩B≠空集应该使a+3>5即a>2
∴2<a<3
综上所述a<-1或2<a<3
2.∵A∪B=R且a<3
∴2a<-1且a+3>5无解
∴不存在a使得A∪B=R
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