# Irrational equation

Algebra Level 5

For $$x,p \in \Re$$, find the maximum value of $$p$$ in which there's real solution for the equation: $\sqrt{x^{2}-p}+2\sqrt{x^{2}-1}=x$ The value of $$x^{2}$$ for such $$p$$ can be written as $$\frac{a}{b}$$, $$a$$, $$b$$ co-prime integers. What is the value of $$a+b$$?

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