Another Inequality #2

Algebra Level 5

\[\large{(a^2 - bc)^2 > k(b^2 - ca)(c^2 - ab)}\]

Find the greatest real number \(k\) such that for any positive \(a,b,c\) with \(a^2 > bc\), the above inequality satisfies. Submit the value of \(k\) upto three correct places of decimals.

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