# Simple Inequality 1

Algebra Level 4

Given that $$a,b,c$$ are non-negative real numbers satisfying $$abc=2$$, then $a\left(b^2+\dfrac{1}{b}\right)+b\left(c^2+\dfrac{1}{c}\right)+c\left(a^2+\dfrac{1}{a}\right)\ge k$ for some integer $$k$$. What is $$k$$?

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