Approach Matters, Answer Doesn't

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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