Almost symmetry!

Algebra Level 4

a4bc+b4ac+c4ab8=a5+b5+c52c4+b4+2a3+4a \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,ba,b and cc are positive real numbers that satisfy the equation above, find the value of a2a^2 .

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