分类：教育/科学-理工学科-数学
问题：不等式求证己知x,y,z&gt;0,求证(y^3+z^3)x^6 
己知x,y,z>0,求证
(y^3+z^3)x^6+(z^3+x^3)y^6+(x^3+y^3)z^6+6(xyz)^3
>=4(xyz)^2*(x^3+y^3+z^3)
回答：己知x,y,z>0,求证 
(y^3+z^3)x^6+(z^3+x^3)y^6+(x^3+y^3)z^6+6(xyz)^3 
>=4(xyz)^2*(x^3+y^3+z^3)

设x=max(x,y,z)或x=min(x,y,z),上式分解为:
[(x^4+y^2*z^2)*(y^3+z^3)+xyz(4y^2*z^2-xy^2-xz^2)](x-y)(x-z)+
x[(x^4+y^2*z^2)*(y^2+3yz+z^2)+x^2(y^4+z^4)+x^2*yz(y^2+z^2)-4xy^2*z^2*(y+z)](y-z)^2>=0