lean_workbook_plus_43932

Well known result: $a=x+y+z\ge xy+yz+zx$ it is: $x^2+y^2+z^2\ge a^2-2a$ it suffices to prove $\frac{a^2-2a+4}{a}\ge 2+\frac{a^2}{3(6+a)}$ which is easy.( $a\ge 3$ )