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A symmetric inequality with a condition

Source: Turkey Junior National Olympiad 2012 P3

December 12, 2012
inequalitiesinequalities proposed

Problem Statement

Let a,b,ca, b, c be positive real numbers satisfying a3+b3+c3=a4+b4+c4a^3+b^3+c^3=a^4+b^4+c^4. Show that aa2+b3+c3+ba3+b2+c3+ca3+b3+c2≥1 \frac{a}{a^2+b^3+c^3}+\frac{b}{a^3+b^2+c^3}+\frac{c}{a^3+b^3+c^2} \geq 1
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