Inequality 46(George Basdekis)

Problem:

Let \displaystyle a,b,c be positive real numbers. Prove that \displaystyle \left(a+\frac{bc}{a}\right)\left(b+\frac{ca}{b}\right)\left(c+\frac{ab}{c}\right)-8abc\geq a(b-c)^2+b(c-a)^2+c(a-b)^2.

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