A Minimum value sum

Algebra Level 3

The minimum value of x4x224x+145+x423x22x+145\sqrt{x^4 - x^2 - 24x + 145} + \sqrt{x^4 - 23x^2 - 2x + 145} can be expressed in the form aba\sqrt{b} , where aa and bb are integers, with bb is not divisible by the square of any prime. What is the value of a+ba+b ?

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