# A Minimum value sum

Algebra Level 4

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

×