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[DOTOANNANG]

Cho $\it{3}$ số thực $\it{a},\,\it{b},\,\it{c}$ thỏa $\it{:}$ $\it{ab}+ \it{bc}+ \it{ca}= \it{4}$ $\it{.}$ Chứng minh $\it{:}$

$$\it{3}\sum \it{a}^{\,\it{2}}- \it{4}\sum \it{a}^{\,\it{4}}\leqq -\,\frac{\it{28}}{\it{3}}$$

$\lceil$ B*W $\it{!}$   $\rfloor$ $\lceil$ S*O*S $\it{!}$ $\rfloor$

Spoiler

$\it{4992}\left [ -\,\it{3}\sum \it{a}^{\,\it{2}}+ \it{4}\sum \it{a}^{\,\it{4}}- \,\frac{\it{28}}{\it{3}} \right ]= \it{3}\sum \it{(}\,\,\it{128}\,\it{a}^{\,\it{2}}+ \it{21}\,\it{ab}- \it{45}\,\it{ac}- \it{240}\,\it{b}^{\,\it{2}}+ \it{24}\,\it{bc}+ \it{112}\,\it{c}^{\,\it{2}}\,\,\it{)}^{\it{2}}+ \it{629}\sum \it{(}\,\,\it{15}\,\it{bc}- \it{7}\,\it{ca}- \it{8}\,\it{ab}\,\,\it{)}^{\,\it{2}}\geqq \it{0}$