Inspired by Alan Yan

Algebra Level 2

If a,b,ca,b,c are positive reals such that abc=1abc=1 , find the minimum value of the following expression:

a2(b+c)+b2(c+a)+c2(a+b)\large a^2(b+c)+b^2(c+a)+c^2(a+b)


Inspiration.
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