Answer: 25

Small Hint:

Set $y=\log_{1995}x,$ so $x=1995^y$

Big Hint:

Compare exponents of $1995$, then use the sum of the two values of $y$

Solution:

Put $y=\log_{1995}x,$ so $x=1995^y.$ The equation becomes $$1995^{\frac{1}{2}+y^2}=1995^{2y},$$ and hence $(y-1)^2=\frac{1}{2}.$ The two values of $y$ have sum $2,$ so the product of the corresponding positive roots is $1995^2.$ Since $1995\equiv-5\pmod {1000},$ its last three digits are $025.$ The requested AIME answer is $25.$