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Let a,b and c be positive real numbers satisfying \min(a+b,b+c,c+a) > \sqrt{2} and a^2+b^2+c^2=3. Prove that

\frac{a}{(b+c-a)^2} + \frac{b}{(c+a-b)^2} + \frac{c}{(a+b-c)^2} \geq \frac{3}{(abc)^2}.

Proposed by Titu Andrescu, Saudi Arabia

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