作业帮x+y=8,xy=15,求x^3y+2x^2y^2+xy^3
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x+y=8,xy=15,求x^3y+2x^2y^2+xy^3
x+y=8,xy=15,求x^3y+2x^2y^2+xy^3
x+y=8,xy=15,求x^3y+2x^2y^2+xy^3
原式=xy(x²+2xy+y²)
=xy(x+y)²
=15×8²
=960
x^3y+2x^2y^2+xy^3
=xy(x^2+2xy+y^2)
=xy(x+y)^2
=15*8^2
=15*64
=960
x³＋2x²y＋xy³=xy(x²＋2xy＋y²)=(xy)(x＋y)²=15×8²=960
x=8-y ， xy=(8-y)y=15则有（y-3)(y-5)=0的y=3或y=5
1）当y=3,x=5时 原试的解为
2）当x=3,y=5时 原试的解为
自己算下就可以了，剩下的都是计算问题了
x³y + 2x²y² + xy³
= (xy)x² + 2(xy)² + (xy)y²
= 15x² + 2×15² + 15y²
= 15(x² + y²) + 450
= 15 {(x+y)² -2xy} + 450
= 15 {8² - 2×15} + 450
= 15 {64 - 30} + 450
= 15×64 - 15×30 + 450
= 15×64
= 960
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