Polynomial saga

Algebra Level 3

x12+x4+x3+x2+x+1x12+1x4+1x3+1x2+1x1\large { x }^{ 12 }+{ x }^{ 4 }+{ x }^{ 3 }+{ x }^{ 2 }+x+{ \frac { 1 }{ { x }^{ 12 } } +\frac { 1 }{ { x }^{ 4 } } }+{ \frac { 1 }{ { x }^{ 3 } } }+{ \frac { 1 }{ { x }^{ 2 } } }+{ \frac { 1 }{ { x }^{ 1 } } }

If xx is a positive real number satisfying x4+1x4=194{ x }^{ 4 }+{ \dfrac { 1 }{ { x }^{ 4 } } }=194, then find the value of the expression above.

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