Inspired From Other

Find the number of ordered pairs of whole numbers \((x,y) \) satisfying \((xy-7)^2 =x^2 +y^2\).

If all these solutions can be expressed as \( (x_1, y_1) , (x_2 , y_2) , \ldots , (x_i , y_i) \), find

\[ x_1 + y_1 + x_2 + y_2 + \cdots + x_i + y_i . \]

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