The number of positive integral solutions of (x, y) when x^2 - 4xy + 6y^2 - 2x - 20y = 29 is

JEE Advanced Mathematics question

The number of positive integral solutions of when is

Answer: (A)

As a quadratic in : , so

x = (2y + 1) ± = 2y + 1 ± = 2y + 1 ±.

For integer , must be a perfect square (and , so ). Trying 6)^2\ldots$,

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Question ID VK-110471