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Fear this inequality! [(b+c)^2 / (a^2+bc) + ... >= 6]

Source: problem 12 (U2) of QEDMO 1; created by Peter Scholze and me

November 7, 2005
inequalitiesfunctioninequalities proposed

Problem Statement

For any three positive real numbers aa, bb, cc, prove the inequality (b+c)2a2+bc+(c+a)2b2+ca+(a+b)2c2+ab≥6.\frac{\left(b+c\right)^{2}}{a^{2}+bc}+\frac{\left(c+a\right)^{2}}{b^{2}+ca}+\frac{\left(a+b\right)^{2}}{c^{2}+ab}\geq 6. Darij
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