Don't Guess 1

Find all the positive integral solutions to the equation $$y^2 = x^2 + x + 2$$.

If the solutions of $$(x,y)$$ are $$(x_1, y_1) , (x_2, y_2) , \ldots, (x_n, y_n)$$, find $$\displaystyle \sum_{i=1}^n x_i y_i$$.

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