olymmath

JBMO-SL 2005 A3

  • Answer

Find the maximum value of the area of a triangle having side lengths a,b,ca, b, c with

a2+b2+c2=a3+b3+c3a^{2}+b^{2}+c^{2}=a^{3}+b^{3}+c^{3}

Dataset text NuminaMath olympiads. Quoted with source.

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S \leq \frac{\sqrt{3}}{4}

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