Cho a,b,c>0 và $a^{2}+b^{2}+c^{2}\doteq 1$. Tìm$ Min$ $a^{7}+b^{7}+c^{7}$
$ Min$ $a^{7}+b^{7}+c^{7}$
Started By khanhlinh97, 27-02-2013 - 20:01
#2
Posted 27-02-2013 - 20:32
Nguyen Duc Thuan
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$\sum \left ( a^7+a^7+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}}\right )\geq \sum 7\sqrt[7]{\frac{a^{14}}{9\sqrt{3}}}=\sum \frac{7}{3\sqrt[4]{3}}a^2=\frac{7}{3\sqrt[4]{3}}$$\Rightarrow \sum a^7\geq \frac{1}{2}(\frac{7}{3\sqrt[4]{3}}-\frac{15}{\sqrt{3}})$Cho a,b,c>0 và $a^{2}+b^{2}+c^{2}\doteq 1$. Tìm$ Min$ $a^{7}+b^{7}+c^{7}$
MOD xoá bài này đi, làm sai !!!
Edited by Nguyen Duc Thuan, 27-02-2013 - 20:34.
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