Inequality 2017

Algebra Level 4

\[\sqrt { \frac { { a }^{ 3 } }{ { a }^{ 3 }+15bcd } } +\sqrt { \frac { { b }^{ 3 } }{ { b }^{ 3 }+15cda } } +\sqrt { \frac { { c }^{ 3 } }{ c^{ 3 }+15dab } } +\sqrt { \frac { { d }^{ 3 } }{ d^{ 3 }+15abc } }\]

Find the minimum value of the expression above, where \(a\), \(b\), \(c\) and \(d\) are positive real numbers.

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