Let be non-negative real numbers satisfying . Show
I got this inequality from an IMO preparation club. I no longer do contest math but still I find this interesting. There is a weird equality case : works (whereas does not).
So far I've tried regrouping terms to disminish the number of variables or the number of non-zero variables. I've shown that the inequality is implied by the three-variable version
if . The three variable version itself is implied by the two variable version, but the two variable version is false.