已知:x+y=5,x^2+y^2=11,求代数式x^3y-2x^2y^2+xy^3的值
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已知:x+y=5,x^2+y^2=11,求代数式x^3y-2x^2y^2+xy^3的值
已知:x+y=5,x^2+y^2=11,求代数式x^3y-2x^2y^2+xy^3的值
已知:x+y=5,x^2+y^2=11,求代数式x^3y-2x^2y^2+xy^3的值
xy=2分之1[(x+y)^2-(x^2+y^2)]
=2分之1×14
=7
x^3y-2x^2y^2+xy^3
=xy(x^2+y^2-2xy)
=7×(11-2×7)
=7×(-3)
=-21
=如有不明白,可以追问
如有帮助,记得采纳,谢谢
已知:x^2+y^2=11
因为:x+y=5,
所以:(x+y)^2=25
即:x^2+y^2+2xy=25
将上述已知代入,有:xy=7
(x^3)y-2(x^2)(y^2)+x(y^3)
=(xy)(x^2+y^2-2xy)
=7×(11-2×7)
=7×(11-14)
=-21
=xy(x^2-2xy+y^2)
另(x+y)^2=25=x^2+y^2+2xy=11+2xy 可推出xy=7
则上式=7*(11-2*7)=-21
不过说实话我觉得这题不对劲,按本题数据计算的话,(x-y)^2=-3,可是一个平方值根本不可能是负的
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