Cho a;b;c >0. CMR:
$\prod (a^{2}-ab+b^{2})\geq \frac{1}{3}abc(\Sigma a^{3})$
Cho a;b;c >0. CMR: $\prod (a^{2}-ab+b^{2})\geq \frac{1}{3}abc(\Sigma a^{3})$
Started By duc321999real, 03-03-2013 - 21:14
#1
Posted 03-03-2013 - 21:14
duc321999real
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- nguyen tien dung 98 likes this
#2
Posted 12-07-2022 - 18:22
TARGET
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$2\sum a^{4}\left (b-c \right )^{2} +\sum a^{2}\left ( b-c \right )^{2}\left ( b+c-a \right )^{2} +\sum \left (b-c \right )^{2}\left (a^2-bc \right )^{2}\geq 0$
- DOTOANNANG and Hoang72 like this
$\sqrt[5]{\frac{a^{5}+b^{5}}{2}}\doteq \sqrt[5]{\frac{a^{5}+b^{5}}{a^{4}+b^{4}}\frac{a^{4}+b^{4}}{a^{3}+b^{3}}\frac{a^{3}+b^{3}}{a^{2}+b^{2}}\frac{a^{2}+b^{2}}{a+b}\frac{a+b}{2}}$
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