**Answer:**

To find the value of x^2, we need to understand the concept of sub duplicate ratio and apply it to the given expression.

**Understanding the Sub Duplicate Ratio:**

The sub duplicate ratio of two quantities is the ratio of their square roots.

Let's say we have two quantities, p and q. The sub duplicate ratio of p and q is given by √p : √q.

**Applying the Sub Duplicate Ratio:**

According to the given statement, the sub duplicate ratio of p-x^2 and q-x^2 is p : q.

Therefore, we can write the equation as:

√(p-x^2) : √(q-x^2) = p : q

**Simplifying the Equation:**

To simplify the equation, we need to eliminate the square roots. We can do this by squaring both sides of the equation:

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

Simplifying further, we get:

p-x^2 : q-x^2 = p^2 : q^2

**Using Cross Multiplication:**

To solve for x^2, we can use cross multiplication.

Cross multiplying the equation, we get:

(p-x^2) * (q^2) = (q-x^2) * (p^2)

Expanding both sides of the equation, we get:

pq^2 - x^2q^2 = qp^2 - x^2p^2

**Simplifying further:**

Rearranging the terms, we get:

pq^2 - qp^2 = x^2p^2 - x^2q^2

Factoring out x^2, we have:

x^2(p^2 - q^2) = pq^2 - qp^2

**Solving for x^2:**

To isolate x^2, we divide both sides of the equation by (p^2 - q^2):

x^2 = (pq^2 - qp^2) / (p^2 - q^2)

This is the value of x^2, which can be calculated using the given values of p and q.

In conclusion, the value of x^2 is (pq^2 - qp^2) / (p^2 - q^2), as derived from the given sub duplicate ratio equation.