lean_workbook_plus_5521

But applying the well-known inequality $u^2+v^2+w^2\geq vw+wu+uv$ to the numbers $u=x^8$ , $v=y^8$ , $w=z^8$ , we obtain $x^{16}+y^{16}+z^{16}\geq\left(yz\right)^8+\left(zx\right)^8+\left(xy\right)^8$ with equality if and only if x = y = z.