y^2=x^3-3x^2+2x x^2=y^3-3x^2+2y 解方程组
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y^2=x^3-3x^2+2x x^2=y^3-3x^2+2y 解方程组
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y^2=x^3-3x^2+2x
x^2=y^3-3y^2+2y
两式相减得:y^2-x^2=(x^3-y^3)-3(x^2-y^2)+2(x-y)
(x-y)(x^2+xy+y^2-2x-2y+2)=0
所以x-y=0,再代入1)式得:x^3-2x^2+2x=0,即x(x^2-2x+2)=0,得:x=0,故y=0,即(0,0)为一组解
或x^2+xy+y^2-2x-2y+2=0,化为x^2+x(y-2)+y^2-2y+2=0
delta=(y-2)^2-4(y^2-2y+2)=y^2-4y+4-4y^2+8y-8=-3y^2+4y-4=-(3y^2-4y+4)
x^2=y^3-3y^2+2y
两式相减得:y^2-x^2=(x^3-y^3)-3(x^2-y^2)+2(x-y)
(x-y)(x^2+xy+y^2-2x-2y+2)=0
所以x-y=0,再代入1)式得:x^3-2x^2+2x=0,即x(x^2-2x+2)=0,得:x=0,故y=0,即(0,0)为一组解
或x^2+xy+y^2-2x-2y+2=0,化为x^2+x(y-2)+y^2-2y+2=0
delta=(y-2)^2-4(y^2-2y+2)=y^2-4y+4-4y^2+8y-8=-3y^2+4y-4=-(3y^2-4y+4)
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