olymmath

ISL 2011 A7

    Let a,ba, b, and cc be positive real numbers satisfying min⁡(a+b,b+c,c+a)>2\min (a+b, b+c, c+a)>\sqrt{2} and a2+b2+c2=3a^{2}+b^{2}+c^{2}=3. Prove that a(b+c−a)2+b(c+a−b)2+c(a+b−c)2≥3(abc)2\frac{a}{(b+c-a)^{2}}+\frac{b}{(c+a-b)^{2}}+\frac{c}{(a+b-c)^{2}} \geq \frac{3}{(a b c)^{2}}

    Dataset text NuminaMath olympiads. Quoted with source.

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