Algebra Level 4

$\large S=\left| \sqrt { { x }^{ 2 }+4x+5 } -\sqrt { { x }^{ 2 }+2x+5 } \right| \quad \forall x \in \mathbb R$

For $$S$$ as given above, find the maximum value of $$S^8$$.

Notation: $$| \cdot |$$ denotes the absolute value function.

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