RMO Question

Algebra Level 3

A=a2+1b+c+b2+1c+a+c2+1a+b\large A=\dfrac{a^2+1}{b+c}+\dfrac{b^2+1}{c+a}+\dfrac{c^2+1}{a+b}

If aa,bb, and cc are three positive real numbers, then find the minimum value of AA.


Source: RMO.
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