已知x+y=1,xy=3/16,求x^3y-2x^2y^2+xy^3的值

已知x+y=1,xy=3/16,求x^3y-2x^2y^2+xy^3的值
已知x+y=1,xy=3/16,求x^3y-2x^2y^2+xy^3的值

已知x+y=1,xy=3/16,求x^3y-2x^2y^2+xy^3的值
x^3y-2x^2y^2+xy^3
=xy(x²-2xy+y²)
=xy(x-y)²
=3/16(x-y)²
=3/16[(x+y)²-4xy]
=3/16(1-3/4)
=3/16x1/4
=3/64
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原式= xy(x²-2xy+y²)
=xy[(x²+2xy+y²)-4xy]
=xy[(x+y)²-4xy]
=3/16*(1²-4*3/16)
=3/64

x³y-2x²y²+xy³
=(xy)(x²-2xy+y²)
=(xy)(x-y)²
=(xy)[(x+y)²-4xy]
=(3/16)×[1²-4×(3/16)]
=3/64

x^3y-2x^2y^2+xy^3=xy(x²-2xy+y²﹚=xy(x－y)²＝xy[﹙x+y﹚²－4xy]=3／16[1²－4×3／16]=3／64