已知（x+y-10)²+根号xy-6=0,求x³y-2x²y²+xy³的值.

已知（x+y-10)²+根号xy-6=0,求x³y-2x²y²+xy³的值.
已知（x+y-10)²+根号xy-6=0,求x³y-2x²y²+xy³的值.

已知（x+y-10)²+根号xy-6=0,求x³y-2x²y²+xy³的值.
∵(x+y-10)²+√(xy-6)=0
∴x+y-10=0,xy-6=0
∴x+y=10,xy=6
x³y+2x²y²+xy³
=xy(x²+2xy+y²)
=xy(x+y)²
=6×10²
=6×100
=600
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