a, b, c-real positive numbers, abc=1. Prove that$\displaystyle \frac {a + b}{2(a^7 + b^7 + c)} +\frac {b + c}{2(b^7 + c^7 + a)}+ \frac {c + a}{2(c^7 + a^7 + b)}<=1$

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- Sep 2nd 2008, 07:17 AMely_enwho can help me with this inequality?
a, b, c-real positive numbers, abc=1. Prove that$\displaystyle \frac {a + b}{2(a^7 + b^7 + c)} +\frac {b + c}{2(b^7 + c^7 + a)}+ \frac {c + a}{2(c^7 + a^7 + b)}<=1$