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    Question

    In the given questions, you will find two equations labeled as I and II. solve both equations and determine the accurate relationship between the variables 'p' and 'q'. Choose the correct option based on your analysis of the solutions.

    I. 25p + 2(2p2 – 1) = 8(p + 5) II.

    8q2 + 35q – 78 = 0
    A p < q Correct Answer Incorrect Answer
    B p > q Correct Answer Incorrect Answer
    C p ≥ q Correct Answer Incorrect Answer
    D p = q or the relationship cannot be established Correct Answer Incorrect Answer
    E p ≤ q Correct Answer Incorrect Answer

    Solution

    ATQ, 25p + 2(2p2 – 1) = 8(p + 5) Or, 25p + 4p2 – 2 = 8p + 40 Or, 4p2 + 17p – 42 = 0 Or, 4p2 + 24p – 7p – 42 = 0 Or, 4p(p + 6) – 7(p + 6) = 0 Or, (4p – 7)(p + 6) = 0 Or, p = (7/4) or -6 From II: 8q2 + 35q – 78 = 0 Or, 8q2 + 48q – 13q – 78 = 0 Or, 8q(q + 6) – 13(q + 6) = 0 Or, (8q – 13)(q + 6) = 0 Or, q = (13/8) or -6 So, no relation can be established between ‘p’ and ‘q’.

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