x+y+z=2,xy+xz+yz=a,xy+z=a,求a的取值范围

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x+y+z=2,xy+xz+yz=a,xy+z=a,求a的取值范围x+y+z=2,xy+xz+yz=a,xy+z=a,求a的取值范围x+y+z=2,xy+xz+yz=a,xy+z=a,求a的取值范围有

x+y+z=2,xy+xz+yz=a,xy+z=a,求a的取值范围
x+y+z=2,xy+xz+yz=a,xy+z=a,求a的取值范围

x+y+z=2,xy+xz+yz=a,xy+z=a,求a的取值范围
有xy+z=a得xy=a-z带入xy+xz+yz=a
得z(x+y-1)=0
由x+y+z=2得x+y=2-z带入上式
得z(1-z)=o
z=0或z=1
当z=0时x+y=2,xy=a
a=(2-x)x=-(x-1)^2+1取值范围为（-无穷,1]
当z=1时x+y=1,xy+x+y=a得a=x(1-x)+1=-(x-1/2)^2+5/4取值范围为（-无穷,5/4]

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