Quadratic equations are getting me tired

Algebra Level 5

Consider an equation with \(p, q\) real roots \(x^{2} - \frac{x}{a} + \frac{1}{b} = 0\).

Also \(\frac{1}{a}, \frac{1}{b}\) are positive integers and \(\frac{1}{a}\geq 2.\)

\([\frac{p}{q}] + [\frac{q}{p}] = (Integer)^{2}\), if and only if (where [.] denotes floor function)

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