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Algebra Level 3

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

Find minimum value of

$\color{darkorange}{\dfrac{a^2+1}{b+c}+\dfrac{b^2+1}{a+c}+\dfrac{c^2+1}{b+a}}$

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by Mehul Chaturvedi

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