# Crazy Gaussian Integral

Calculus Level 5

If the following integral is satisfied for some relationship between the constants $$a , b$$ and $$c$$-

$\displaystyle\int_{-∞}^{∞}\displaystyle\int_{-∞}^{∞} e^{-(ax^{2} + 2bxy + cy^{2})}dxdy = 1$

Find the value of $$b^{2} -ac$$

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