INEQUALITY'S BLOG

August 1, 2010

Problem 046

Filed under: Uncategorized — KKKVVV @ 11:32 pm

Let a, b, c\geq 0 ; a\leq b\leq c and s\geq r\geq 0; s\geq 2. Prove that:

\displaystyle \biggl(\frac{a^rb^s+b^rc^s+c^ra^r}{3}\biggl)\biggl(\frac{a^{s-r}+b^{s-r}+c^{s-r}}{3}\biggl)\geq \biggl(\frac{ab+bc+ca}{3}\biggl)^s

 

Van Khea          

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