USA 97 [1/(b^3+c^3+abc) + ... >= 1/(abc)]
Source: USAMO 1997/5; also: ineq E2.37 in Book: Inegalitati; Authors:L.Panaitopol,V. Bandila,M.Lascu
September 12, 2003
inequalitiesAMCUSA(J)MOUSAMOsymmetrythree variable inequalityHi
Problem Statement
Prove that, for all positive real numbers , , , the inequality
\frac {1}{a^3 \plus{} b^3 \plus{} abc} \plus{} \frac {1}{b^3 \plus{} c^3 \plus{} abc} \plus{} \frac {1}{c^3 \plus{} a^3 \plus{} abc} \leq \frac {1}{abc}
holds.