lean_workbook_plus_68013

for all real $x,y,z$ prove or disprove that \n\n $x^4+y^4+z^4+3(x^2y^2+x^2z^2+y^2z^2)\geq 2(x^3(y+z)+y^3(x+z)+z^3(x+y))$ \n\n $x^4+y^4+z^4+3(x^2y^2+x^2z^2+y^2z^2)-2(x^3(y+z)+y^3(x+z)+z^3(x+y))=$ \n\n $=(x^2+y^2+z^2-xy-xz-yz)^2=\frac{1}{2}((x-y)^4+(y-z)^4+(z-x)^4).$