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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