# An inequality problem by Gurido Cuong

Algebra Level 5

$\dfrac{1}{\sqrt[3]{a+3b}}+\dfrac{1}{\sqrt[3]{b+3c}}+\dfrac{1}{\sqrt[3]{c+3a-d}}-24abc+12abcd$ If $$a,b$$ and $$c$$ are positive reals satisfying $$a+b+c=\dfrac{3}{4}$$ and $$d$$ is a non-negative real, minimize the expression above to 3 decimal places

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