已知x+y=-2,xy=5.求x^3y+2x^2y^2+xy^3的值.

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已知x+y=-2,xy=5.求x^3y+2x^2y^2+xy^3的值.
已知x+y=-2,xy=5.求x^3y+2x^2y^2+xy^3的值.

已知x+y=-2,xy=5.求x^3y+2x^2y^2+xy^3的值.
x^3y+2x^2y^2+xy^3
=xy(x^2+2xy+y^2)
=xy(x+y)^2
=5*(-2)^2
=5*4
=20.

x³y+2x²y²+xy³
=xy(x²+2xy+y²)
=xy(x+y)²
=5(-2)²
=5×4
=20

x^3y+2x^2y^2+xy^3=xy(x+y)^2=5*(-2)^2=20

x^3y+2x^2y^2+xy^3=xy(x^2+2xy+y^2)
=(xy)(x+y)^2
=(5)(-2)^2
=20

x+y=-2->x^2+y^2+2xy=4
xy=5
则有x^2+y^2=-6
所以解出来x,y是虚数
(x-y)^2=-16
x-y=16i
x=-1+4i
y=-1-4i
后面自己代结果20
也可以化为(xy)(x+y)^2=20

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