bump.....

Perhaps this topic will contribute a little to solving this problem. I have seen a topic with a proof that for $n$ real variables the greatest coefficient can be expressed in a closed form as $k_{max}(n)=\frac{1}{\cos\frac{\pi}{n+1}}$ but I cannot find that topic right now. The next step would be a formal proof that the intervals $\left[-k_{max}(n),k_{max}(n)\right]$ contain all and only the valid values of the coefficient for a given $n$.

(a) $p\le \sqrt{2}$ $x_1=\sqrt{2},x_2=2, x_3=\sqrt{2} \rightarrow p\le \sqrt{2}$ For $p=\sqrt{2}$, By AM-GM $$LHS =x_1^2+\frac{x_2^2}{2}+\frac{x_2^2}{2}+x_3^2\ge \sqrt{2}x_1x_2+\sqrt{2}x_2x_3$$

Is this topic you are referring to? @2above

No, the one I had in mind was older and contained pictures with the proof in Chinese or links to such pictures.

This seems nice, although obviously not the post @above is referring to.