已知:x-y=6 xy=3 求x³y²-x²y³

已知:x-y=6 xy=3 求x³y²-x²y³
已知:x-y=6 xy=3 求x³y²-x²y³

已知:x-y=6 xy=3 求x³y²-x²y³
解
x-y=6
两边平方
x²-2xy+y²=36
∵xy=3
∴x²+y²=36+2xy=36+6=42
∴x³y+xy³
=xy(x²+y²)
=3×42
=126

∵x-y=6;xy=3
∴x³y²-x²y³
=x²y²(x-y)
=(xy)²×(x-y)
=3²×6
=9×6
=54