Minimize the Expression 2

Algebra Level 4

Given that a,b,c>0a, b, c > 0 , minimize: a2+12a+b+b2+12b+c+c2+12c+a. \dfrac{a^2+1}{2a+b}+ \dfrac{b^2+1}{2b+c}+ \dfrac{c^2+1}{2c+a}.

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