Approach Matters, Answer Doesn't

Algebra Level 3

S=x2+4x+5x2+2x+5xR \large S=\left| \sqrt { { x }^{ 2 }+4x+5 } -\sqrt { { x }^{ 2 }+2x+5 } \right| \quad \forall x \in \mathbb R

For SS as given above, find the maximum value of S8S^8.

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

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