What kind of Sorcery is this ?

Algebra Level 5

Consider: \[ a = \sqrt{x^2 -5x +6} \] \[ b = \sqrt{x^2 -5x +4} \]

Such that,

\[ \left( a + b \right)^{\dfrac{x}{2}} + \left( a - b \right)^{\dfrac{x}{2}} = 2^{ \left( \dfrac{x+4}{4} \right) } \]

Find the predecessor of the sum of all values of x satisfying the given equation.

Question inspired from: Cengage - Algebra

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