Question

    If {x + (1/x)} = 8, then find the value of {x 4

     + (1/x 4 )}.
    A 3842 Correct Answer Incorrect Answer
    B 3642 Correct Answer Incorrect Answer
    C 3542 Correct Answer Incorrect Answer
    D 3742 Correct Answer Incorrect Answer

    Solution

    {x + (1/x)} = 8

    Squaring both sides,

    Using (a + b) 2  = a 2  + 2ab + b 2

    {x + (1/x)} 2  = 8 2

    So, x 2  + (1/x 2 ) + 2 × (x) × (1/x) = 64

    Or, x 2  + (1/x 2 ) + 2 = 64

    Or, x 2  + (1/x 2 ) = 64 – 2 = 62

    Again squaring both sides,

    {x 2  + (1/x 2 )} 2  = 62 2

    So, x 4  + (1/x 4 ) + 2 × (x 2 ) × (1/x 2 ) = 3844

    Or, x 4  + (1/x 4 ) + 2 = 3844

    Or, x 4  + (1/x 4 ) = 3844 – 2 = 3842

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