解下列不等式1<x2-3x+1<9-x

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解下列不等式1<x2-3x+1<9-x
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解下列不等式1<x2-3x+1<9-x
解下列不等式1<x2-3x+1<9-x

解下列不等式1<x2-3x+1<9-x
解:

x^2-3x+1>1
x^2-3x>0
x(x-3)>0
x∈(负无穷,0)∪(3,正无穷)

x^2-3x+1

1<x2-3x+1<9-x
∴﹛x²-3x+1>1 x²-3x>0 x(x-3)>0 x<0或x>3
x²-3x+1<9-x x²-2x-8<0 (x-4)(x+2)<0 -2<x<4
∴-2<x<0或3<x<4