Prove $\sum\limits_{cyc}\left(\frac{a^4}{a^3+b^3}\right)^{\frac34} \geqslant \frac{a^{\frac34}+b^{\frac34}+c^{\frac34}}{2^{\frac34}}$ Posted by HN_NH, at math.stackexchange.com, 21 May 2016 When $a,b,c > 0$…