已知x+y=4,x^2+y^2=14,求x^3 y-2x^2y^2+xy^3
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已知x+y=4,x^2+y^2=14,求x^3 y-2x^2y^2+xy^3
已知x+y=4,x^2+y^2=14,求x^3 y-2x^2y^2+xy^3
已知x+y=4,x^2+y^2=14,求x^3 y-2x^2y^2+xy^3
2xy=(x+y)^2-(x^2+y^2)=16-14=2
xy=1
x^3 y-2x^2y^2+xy^3 =xy(x^2+y^2-2xy)=1*(14-2)=12
【1】x+y=4.∴x²+y²=(x+y)²-2xy=16-2xy=14.===>xy=1.【2】原式=xy(x²+y²)-2(xy)²=1×14-2×1²=12.
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