INEQUALITY'S BLOG

July 27, 2010

(Van Khea):Problem 015

Filed under: the new math — KKKVVV @ 5:11 pm

Let a, b, c>0 ; a^2+b^2+c^2=1. Prove that:

\displaystyle \frac{bc}{a^{4}}+\frac{ca}{b^{4}}+\frac{ab}{c^{4}}+\biggl(\frac{1}{a}+\frac{1}{b}\biggl)\biggl(\frac{1}{b}+\frac{1}{c}\biggl)\biggl(\frac{1}{c}+\frac{1}{a}\biggl)\geq 3(8\sqrt{3}+3)

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