Cho $\it{3}$ số không âm và có dạng $\it{ab}+ \it{bc}+ \it{ca}\neq 0$ . Chứng minh rằng:
$$\sum\limits_{cyc}\frac{\it{a}}{\sqrt[\it{3}\,]{\left ( \it{a}+ \it{b} \right )^{\,\it{2}}\,\left ( \it{a}+ \it{b}+ \it{c} \right )}}\leqq \it{1}+ \frac{\it{2}}{\it{9}}\,\sqrt{\,\it{3}}$$
$$\sum\limits_{cyc}\frac{\it{a}}{\sqrt[\it{4}\,]{\left ( \it{a}+ \it{b} \right )^{\,\it{3}}\,\left ( \it{a}+ \it{b}+ \it{c} \right )}}\leqq \it{1}+ \frac{\it{64}\,\sqrt{\,\it{5}}}{\it{125}}$$