.已知集合A={x丨2x2+3x+1=0},B={x丨m2x2+(m+2)x+1=0},若AUB=A,求实数A的取值范围.
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![.已知集合A={x丨2x2+3x+1=0},B={x丨m2x2+(m+2)x+1=0},若AUB=A,求实数A的取值范围.](/uploads/image/z/3143854-46-4.jpg?t=.%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7Bx%E4%B8%A82x2%2B3x%2B1%3D0%7D%2CB%3D%7Bx%E4%B8%A8m2x2%2B%EF%BC%88m%2B2%29x%2B1%3D0%7D%2C%E8%8B%A5AUB%3DA%2C%E6%B1%82%E5%AE%9E%E6%95%B0A%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
.已知集合A={x丨2x2+3x+1=0},B={x丨m2x2+(m+2)x+1=0},若AUB=A,求实数A的取值范围.
.已知集合A={x丨2x2+3x+1=0},B={x丨m2x2+(m+2)x+1=0},若AUB=A,求实数A的取值范围.
.已知集合A={x丨2x2+3x+1=0},B={x丨m2x2+(m+2)x+1=0},若AUB=A,求实数A的取值范围.
A={x丨2x2+3x+1=0}={x丨(x+1)(2x+1)=0}={-1,-1/2},
AUB=A,所以B⊆A
1、若B={-1},则m2-(m+2)+1=0,m2-m-1=0解之得m=(1+- √5)/2
2、若B={-1/2},则1/4m2-1/2(m+2)+1=0,m2-2m=0解之得m=0或2
3、若B={-1,-1/2},则-1-1/2=-(m+2)/m2,-1*(-1/2)=1/m2
无解
综上所述,实数m的取值范围为{(1+√5)/2,(1- √5)/2,0,2}
2X^2+3X+1=0
(X+1)(2X+1)=0
x=-1或x=-1/2 A={-1,-1/2}
2mX^2+(m+2)X+1=0
m=o B=空集满足
(2X+1)(mX+1)=o
X=-1/2或X=-I/m
所以B={-1/2,-1/m} 当m=1或m=2时满足
所以m∈{0,1,2}
解2x^2+3x+1=0得x=-1或-1/2,
∴A={x|x=-1或-1/2}
∵A∪B=A,∴B={x|x=-1或-1/2}或B=空集
∴将x=-1或-1/2代入m^2x^2+(m+2)x+1=0,
得m^2-(m+2)+1=0或1/4m^2-1/2(m+2)+1=0,
解得m=0,2,(1±√5)/2
又∵B=空集,
∴有(m+2)^2...
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解2x^2+3x+1=0得x=-1或-1/2,
∴A={x|x=-1或-1/2}
∵A∪B=A,∴B={x|x=-1或-1/2}或B=空集
∴将x=-1或-1/2代入m^2x^2+(m+2)x+1=0,
得m^2-(m+2)+1=0或1/4m^2-1/2(m+2)+1=0,
解得m=0,2,(1±√5)/2
又∵B=空集,
∴有(m+2)^2-4×m^2×1<0
解得m<-2/3或m>2
综上所述m的取值范围是{m|m<-2/3或m>2}
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