Inequality

Algebra Level 3

If \(a,b,c\in \mathbb R^{+}\), then find the minimum value of

\[\frac{a^{4}+1}{(b+c)^{2}}+\frac{b^{4}+1}{(c+a)^{2}}+\frac{c^{4}+1}{(a+b)^{2}}\]

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