If p and q are real numbers such that p2 + (p - 2q - 1)2 = - 4q(p +
q), then the value p - 2q is

Let's solve the given equation step by step: Given: On Expanding the Equation (p−2q−1)² , we get

Substituting back into the equation:

On Combine all p² terms, we get:

Let Assume a simple relation:

Assume p - 2q = k (where k is a constant we need to find). Then = If k = 1, substitute p = 2q + k = 2q+1. Then, Substitute p=2q+1 into both sides: Simplify to verify if the equation holds true. Hence, it's shows that the equation is satisfied. therefore, The value of p − 2q is 1.