# Maximize a Constant in an Inequality with a Restriction

Algebra Level 4

Real numbers $$a$$, $$b$$, and $$c$$ satisfy $$abc=1$$. Given that $$k$$ is an integer $$\geq 2$$, find the maximum possible $$R$$ that satisfies

$\dfrac{a^k}{a+b}+\dfrac{b^k}{b+c}+\dfrac{c^k}{c+a} \geq R$

for all $$a$$, $$b$$, and $$c$$ satisfying the condition previously stated.

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