# 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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