已知x+y=-2,a+b=-1/2,x^2-xy+y^2=-1,求bx^3+ay^3+by^3+ax^3的值

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已知x+y=-2,a+b=-1/2,x^2-xy+y^2=-1,求bx^3+ay^3+by^3+ax^3的值

已知x+y=-2,a+b=-1/2,x^2-xy+y^2=-1,求bx^3+ay^3+by^3+ax^3的值
已知x+y=-2,a+b=-1/2,x^2-xy+y^2=-1,求bx^3+ay^3+by^3+ax^3的值

已知x+y=-2,a+b=-1/2,x^2-xy+y^2=-1,求bx^3+ay^3+by^3+ax^3的值
bx^3+ay^3+by^3+ax^3=(a+b)^3+(a+b)y^3=-1/2x^3--2y^3=-1/2(x^3+y^3)
由a³+b³=(a+b)(a²-ab+b²)
可得-1/2(x^3+y^3)=-1/2{(x+y)(x^2-xy+y^2)}=-1/2*(-2)*-1=-1

bx^3+ay^3+by^3+ax^3=(a+b)(x^3+y^3)=(a+b)(x+y)(x^2-xy+y^2)=-1