Cyclic Inequality #2

Algebra Level 5

\[\large{ \dfrac{b^2c^2}{a^2(a-b)(a-c)} + \dfrac{c^2a^2}{b^2(b-c)(b-a)} + \dfrac{a^2b^2}{c^2(c-a)(c-b)} > K }\]

Find the greatest constant \(K\) upto three places of decimals such that the above inequality satisfies for all distinct positive real numbers \(a,b,c\).

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