Square Root Equals Trouble

Algebra Level 3

If a,b,c>0a,b,c > 0 and a+b+c=3a+b+c=3, find the minimum value of a2+bc+2+b2+ac+2+c2+ab+2\sqrt{a^2 + bc + 2} + \sqrt{b^2 + ac + 2} + \sqrt{c^2 + ab+ 2}.

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