已知y=1/3x-1 求1/3x^2-2xy^2-2的值

解答：

x=3(y+1)

原式=3(y+1)^2-6(y+1)*y^2-2
=3y^2+6y+3-6y^3-6y^2-2
=-6y^3-3y^2-1

1/3x2-2xy+3y2-2
=1/3(x^2-6xy+9y^2)-2
=1/3(x-3y)^2-2
=1/3〔x-3(1/3x-1)〕^2-2
=1/3(x-x+3)^2-2
=3-2
=1

3(y+1)=x
原式=3(y+1)^2-6(y+1)*y^2-2
=3y^2+6y+3-6y^3-6y^2-2
=-6y^3-3y^2-1

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