# 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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