Are you smarter than me? 45

Algebra Level 3

If a,b,c\color{#3D99F6}{a,b,c} are positive integers

Find minimum value of

a2+1b+c+b2+1a+c+c2+1b+a\color{darkorange}{\dfrac{a^2+1}{b+c}+\dfrac{b^2+1}{a+c}+\dfrac{c^2+1}{b+a}}

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