Approach Matters, Answer Doesn't

Algebra Level 4

If \[ S=\left| \sqrt { { x }^{ 2 }+4x+5 } -\sqrt { { x }^{ 2 }+2x+5 } \right| \quad \forall \quad x\epsilon R\\\] Then find the maximum value of \( { S }^{ 8 }\).

Details and Assumptions:

\(\left| a \right|\) means modulus of \( a\).

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