(xy+yz+zx)^2=x^2y^2+y^2z^2+z^2x^2+2xyz(x+y+z)=1x^2y^2+y^2z^2+z^2x^2=1/3(x^2y^2+y^2z^2+z^2x^2)(1+1+1)≥1/3(xy+yz+zx)^2=1/3（柯西不等式）所以xyz(x+y+z)≤1/3
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