已知（x+y-10)²+√(xy-6)=0求x³y-2x²y²+xy³

已知（x+y-10)²+√(xy-6)=0求x³y-2x²y²+xy³
已知（x+y-10)²+√(xy-6)=0求x³y-2x²y²+xy³

已知（x+y-10)²+√(xy-6)=0求x³y-2x²y²+xy³
（x+y-10)²+√(xy-6)=0
∴{x+y-10=0
xy-6=0
即{x+y=10
xy=6
x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy(x²+2xy+y²-4xy)
=xy[(x+y)²-4xy]
=6×(10²-4×6)
=456

（x+y-10)²+√(xy-6)=0
（x+y-10)²>=0,√(xy-6)>=0
两个非负数之和为0，只能同时为0才能成立。所以：
（x+y-10)²=√(xy-6)=0
x+y=10,xy=6
x³y-2x²y²+xy³
=xy(x²-2xy+y²)...

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（x+y-10)²+√(xy-6)=0
（x+y-10)²>=0,√(xy-6)>=0
两个非负数之和为0，只能同时为0才能成立。所以：
（x+y-10)²=√(xy-6)=0
x+y=10,xy=6
x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy[(x²+2xy+y²)-4xy]
=xy[(x+y)²-4xy]
=6*(100-24)
=456

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