Euler 's 13 elements!

Algebra Level 4

Given

\[\large \begin{cases} a = -\sqrt { 99 } + \sqrt { 999 } + \sqrt { 9999 } \\ b = \sqrt { 99 } - \sqrt { 999 } + \sqrt { 9999 } \\ c = \sqrt { 99 } + \sqrt { 999 } -\sqrt { 9999 } \end{cases} \]

then find the value of

\[\frac { { a }^{ 4 } }{ \left( a - b \right) \left( a - c \right) } + \frac { { b }^{ 4 } }{ \left( b - c \right) \left( b - a \right) } + \frac { { c }^{ 4 } }{ \left( c - a \right) \left( c - b \right) }\].

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