设集合A={x|x2-3x+2=0},B={x|x2+2(a+1)x+(a2-5)=0},若U=R,A∩(∁UB)=A,求实数a的取值范围.
人气:366 ℃ 时间:2020-06-14 04:45:14
解答
∵A∩(∁UB)=A,∴A⊆∁UB,∴A∩B=∅,①若B=∅,则△<0⇒a<-3适合;②若B≠∅,则a=-3时,B={2},A∩B={2},不合题意;当a>-3,此时需1∉B且2∉B,将2代入B的方程得a=-1或a=-3;将1代入B的方程得a2+2a-2=0⇒a...
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