Introduction:
In mathematics, the sub duplicate ratio is a ratio of two quantities such that the square of the larger quantity is equal to the product of the two quantities. In this question, we are given two quantities p-x^2 and q-x^2 and we need to find their sub-duplicate ratio.

Solution:
To find the sub duplicate ratio of p-x^2 and q-x^2, we need to follow the given steps:

Step 1: Find the square root of p-x^2 and q-x^2.
Let A = √(p-x^2) and B = √(q-x^2)

Step 2: Find the ratio of A and B.
The sub duplicate ratio of p-x^2 and q-x^2 is A:B or √(p-x^2) : √(q-x^2).

Step 3: Simplify the ratio.
We can simplify the ratio by multiplying both the numerator and denominator by the square root of (p+x^2) and (q+x^2) respectively.

Hence, the sub duplicate ratio of p-x^2 and q-x^2 is:

√(p-x^2) : √(q-x^2)
= √(p-x^2) * √(q+x^2) : √(q-x^2) * √(q+x^2)
= √(p^2-q^2+x^2q-x^2p) : √(q^2-p^2+x^2q-x^2p)

Conclusion:
In conclusion, we can say that the sub duplicate ratio of p-x^2 and q-x^2 is √(p^2-q^2+x^2q-x^2p) : √(q^2-p^2+x^2q-x^2p).