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 $$a$$.

×