What kind of Sorcery is this ?

Algebra Level 5

Consider: a=x25x+6 a = \sqrt{x^2 -5x +6} b=x25x+4 b = \sqrt{x^2 -5x +4}

Such that,

(a+b)x2+(ab)x2=2(x+44) \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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