Almost symmetry!

Algebra Level 4

\[ \large \frac { \frac { { a }^{ 4 } }{ bc } +\frac { { b }^{ 4 } }{ ac } +\frac { { c }^{ 4 } }{ ab } }{ 8 } =\frac { { a }^{ 5 }+{ b }^{ 5 }+{ { c }^{ 5 } } }{ 2{ c }^{ 4 }+{ b }^{ 4 }+2{ a }^{ 3 }+4a } \]

If \(a,b\) and \(c\) are positive real numbers that satisfy the equation above, find the value of \(a^2 \).

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