If the roots of the equation $\left( a-1 \right) { \left( { x }^{ 2 }+x+1 \right) }^{ 2 }=\left( a+1 \right) \left( { x }^{ 4 }+{ x }^{ 2 }+1 \right) $ are real and distinct then the value of $a\in $

By factoring x^4 + x^2 + 1 as (x^2 + x + 1)(x^2 - x + 1) and dividing both sides by the non-zero term x^2 + x + 1, the equation simplifies to x^2 - ax + 1 = 0. For this quadratic equation to have real and distinct roots, its discriminant must be strictly positive, which yields a^2 - 4 > 0, or a in (-infinity, -2) U (2, infinity).