已知x+y=2 xy=1\2求x^3y-2x^2y^2+xy^3
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![已知x+y=2 xy=1\2求x^3y-2x^2y^2+xy^3](/uploads/image/z/3739669-61-9.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%3D2+xy%3D1%5C2%E6%B1%82x%5E3y-2x%5E2y%5E2%2Bxy%5E3)
已知x+y=2 xy=1\2求x^3y-2x^2y^2+xy^3
已知x+y=2 xy=1\2求x^3y-2x^2y^2+xy^3
已知x+y=2 xy=1\2求x^3y-2x^2y^2+xy^3
(x-y)²
=x²+y²-2xy
=(x+y)²-4xy
=2²-2
=2
所以:
x^3y-2x^2y^2+xy^3
=xy(x²-2xy+y²)
=xy(x-y)²
=(1/2)•2
=1
x??y-2x??Y??+xy??=xy(x??-2xy+y??)=xy(x-y)??x+y=1,xy=3/16(x-y)??=1-3/4=1/4故原式=3/16×﹙1/4﹚=3/64