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    Question

    If [x + (1/x)] = 7, find the value of [x⁴ +

    (1/x⁴)].
    A 1,201 Correct Answer Incorrect Answer
    B 6.520 Correct Answer Incorrect Answer
    C 2,207 Correct Answer Incorrect Answer
    D 5,450 Correct Answer Incorrect Answer

    Solution

    ATQ,

    x + (1/x) = 7

    Squaring both sides:

    [x + (1/x)]² = 7²

    Using identity: (a + b)² = a² + 2ab + b²

    x² + (1/x²) + 2 = 49

    So, x² + (1/x²) = 49 - 2 = 47

    Squaring again:

    [x² + (1/x²)]² = 47² = 2,209

    So, x⁴ + (1/x⁴) + 2 = 2,209

    Therefore, x⁴ + (1/x⁴) = 2,209 - 2 = 2,207

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