已知集合A={x|x²-(3a+3)x+2(3a+1)<0,x∈R},B={x|x-2a/x-(a²+1) <0,x∈R} 10
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已知集合A={x|x²-(3a+3)x+2(3a+1)<0,x∈R},B={x|x-2a/x-(a²+1)<0,x∈R}1.求当4不∈B时,实数a的取值范围,2.求使B包含于A的实数a的取值范围(1)解析:∵B={x|(x-2a)/[x-(a^2+1)]<0,x∈R}x≠a^2+1
∵a^2+1-2a=(a-1)^2>=0
∴当a=1时,2a=a^2+1,
B={}
当a≠1时,2a<a^2+1
2a<x<a^2+1
∵4不∈B
A^2+1<4==>-√3<a<√3
2a>4==>a>2
二者交为空
∴a无论为何值,4∈B
(2)解析:∵集合A={x|x^2-(3a+3)x+2(3a+1)<0,x∈R},x^2-(3a+3)x+2(3a+1)=0==>x1=3a+1,x2=2∴当a>=1/3时,2<=x<=3a+1;∵2a<x<a^2+12a>=2==>a>=1A^2+1<=3a+1==>0<=a<=3取三者交1<=a<=3当a<1/3时,3a+1<x<2
2a>3a+1==>a<=-1
A^2+1<=2==>-1<=a<=1
取三者交a=-1
综上B包含于A的实数a的取值范围a=-1或1<=a<=3
∵a^2+1-2a=(a-1)^2>=0
∴当a=1时,2a=a^2+1,
B={}
当a≠1时,2a<a^2+1
2a<x<a^2+1
∵4不∈B
A^2+1<4==>-√3<a<√3
2a>4==>a>2
二者交为空
∴a无论为何值,4∈B
(2)解析:∵集合A={x|x^2-(3a+3)x+2(3a+1)<0,x∈R},x^2-(3a+3)x+2(3a+1)=0==>x1=3a+1,x2=2∴当a>=1/3时,2<=x<=3a+1;∵2a<x<a^2+12a>=2==>a>=1A^2+1<=3a+1==>0<=a<=3取三者交1<=a<=3当a<1/3时,3a+1<x<2
2a>3a+1==>a<=-1
A^2+1<=2==>-1<=a<=1
取三者交a=-1
综上B包含于A的实数a的取值范围a=-1或1<=a<=3
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