如果x+y=0,xy=-7 问:x^2y+xy^2= ,x^2+y^2=

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如果x+y=0,xy=-7 问:x^2y+xy^2= ,x^2+y^2=
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如果x+y=0,xy=-7 问:x^2y+xy^2= ,x^2+y^2=
如果x+y=0,xy=-7 问:x^2y+xy^2= ,x^2+y^2=

如果x+y=0,xy=-7 问:x^2y+xy^2= ,x^2+y^2=
x+y=0
(x+y)^2=x^2+y^2+2xy=0
x^2+y^2=-2xy=-2(-7)=14
x^2y+xy^2=xy(x+y)=(-7)*0=0
x^2+y^2=14

x^2y+xy^2
=xy(x+y)
=(-7)*0
=0
x^2+y^2
=(x+y)^2-2xy
=0+14
=14

非常简单:x^2=y^2=7,代入两式,得
0
14

x^2y+xy^2
=xy(x+y)
=0*(-7)
=0
x^2+y^2
=(x+y)^2-2xy
=(-7)^2-2*0
=49