Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.2 National olympiad Prove it

75. Given $a b c \neq 0$ , prove: $\frac{a^{4}}{4 a^{4}+b^{4}+c^{4}}+\frac{b^{4}}{a^{4}+4 b^{4}+c^{4}}+\frac{a^{4}}{a^{4}+b^{4}+4 c^{4}} \leqslant \frac{1}{2}$ . (2004 Beijing Mathematical Competition Problem)

Solution

None

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