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    Question

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

    A 2 Correct Answer Incorrect Answer
    B 1 Correct Answer Incorrect Answer
    D -1 Correct Answer Incorrect Answer

    Solution

    ATQ,

    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.

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