Mahalanobis distance between two multivariate Gaussian distribution

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The Mahalanobis distance is a measure of the distance between a point P and a distribution D, can it be used to measure the distance of two MVG model? how to deduce the function below? enter image description here

From wiki, the first term of Bhattacharyya distance is a squared Mahalanobis distance: enter image description here However, I don't know how to deduce that function.

Thanks!

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