Konigsberg wrote: Given real numbers $x$, $y$, $z$ such that $xyz=-1$, show that $x^4+y^4+z^4+3(x+y+z) \ge \sum_{sym} \frac{x^2}{y}$. It's $(x+y+z)^2\sum_{cyc}(x^2-xy)\geq0$, which is obvious.