Inequality with large range

Algebra Level 5

$\large (a+bc)^{ 2 } + (b+ca)^{ 2 } + (c+ab)^{ 2 } \geq \sqrt { k } (a+b)(b+c)(c+a)$

For positive real $$a$$, $$b$$ and $$c$$, find the maximum $$k$$ such that the above inequality is true.

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