Minimium

Algebra Level 3

If \(a\), \(b\), and \(c\) are positive real numbers such that \(a^2+b^2+c^2=1\), then find the minimum value of the following expression \[\frac{a^2}{1+2bc}+\frac{b^2}{1+2ca}+\frac{c^2}{1+2ab} \]

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