简单高一集合~!已知集合A={x|10/x+3≥1,x属于R},B={x|x²-(3a-1)x+2a²
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简单高一集合~!
已知集合A={x|10/x+3≥1,x属于R},B={x|x²-(3a-1)x+2a²-a<0}若B∪A+A,求实数a的取值范围
是B并A=A
已知集合A={x|10/x+3≥1,x属于R},B={x|x²-(3a-1)x+2a²-a<0}若B∪A+A,求实数a的取值范围
是B并A=A
A={x|10/x+3≥1,x属于R}
= { x| (7-x)/(x+3)≥0 ,x属于R}
= { x| -3< x ≤ 7 }
B={x|x²-(3a-1)x+2a²-a<0}
= { x| x²-(3a-1)x+a(2a-1)<0}
= { x| (x-a)(x-(2a-1))< 0 }
if a< 2a-1
ie a > 1
then
B= { x| a< x < 2a-1}
if a B is subset of A
if a a > -3 and 2a-1≤ 7
=> a > -3 and a ≤ 4
ie -3 1
=> 2a-1 > -3 and a ≤ 7
=> a > -1 and a ≤ 7
ie 1< a ≤ 7
if a=1
B = ø is subset of A
Combine, we get
-3 -3
= { x| (7-x)/(x+3)≥0 ,x属于R}
= { x| -3< x ≤ 7 }
B={x|x²-(3a-1)x+2a²-a<0}
= { x| x²-(3a-1)x+a(2a-1)<0}
= { x| (x-a)(x-(2a-1))< 0 }
if a< 2a-1
ie a > 1
then
B= { x| a< x < 2a-1}
if a B is subset of A
if a a > -3 and 2a-1≤ 7
=> a > -3 and a ≤ 4
ie -3 1
=> 2a-1 > -3 and a ≤ 7
=> a > -1 and a ≤ 7
ie 1< a ≤ 7
if a=1
B = ø is subset of A
Combine, we get
-3 -3
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