x^2-x+1>1/3x(x-1)一元二次不等式3x^2-3x+1>-3/2x^2

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x^2-x+1>1/3x(x-1)一元二次不等式3x^2-3x+1>-3/2x^2

x^2-x+1>1/3x(x-1)一元二次不等式3x^2-3x+1>-3/2x^2
x^2-x+1>1/3x(x-1)一元二次不等式
3x^2-3x+1>-3/2x^2

x^2-x+1>1/3x(x-1)一元二次不等式3x^2-3x+1>-3/2x^2
3x^2-3x+1>-3/2x^2
移项、合并同类项得
5/2x²-3x+1>0
(5/2x-1)(1/2x-1)>0
所以5/2 x-1>0,1/2 x-1>0或5/2 x-10
配方得:(x-1/2)²+5/4>0
所以x可取一切实数
即原不等式组的解集是R