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[phamduytien]

1.Cho a,b,c>0 thoả mãn $a^{4}+b^{4}+c^{4}\geq a^{3}+b^{3}+c^{3}$.

Chứng minh: $\sum \frac{a^{3}}{\sqrt{b^{4}+b^{2}c^{2}+c^{4}}}\geq \sqrt{3}$

(Ba Lan, 2010)

2.Cho a,b,c > thoả mãn $a+b+c\geq \frac{1}{a}+\frac{1}{b}+\frac{1}{c}$

Chứng minh $a+b+c\geq \frac{3}{a+b+c}+\frac{2}{abc}$

(Peru, 2007)