证明:x、y、z>0,依Cauchy不等式,得(x^2+y^2+z^2)(y^2+z^2+x^2)>=(xy+yz+zx)^2--->x^2+y^2+z^2>=xy+yz+zx.故对原式再用Cauchy不等式,得[x(x+y)+y(y+z)+z(z+x)][x^3/(x+y)+y^3/(y+z)+z^3/(z+x)]>=(x^2+y^2+z^2)^2--->x...