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    Question

    If x 8  + x -8  = 194, then find

    the value of (2x 2  – 4) 2  – 1.
    A 11 Correct Answer Incorrect Answer
    B -27 Correct Answer Incorrect Answer
    C 16 Correct Answer Incorrect Answer
    D None of the above Correct Answer Incorrect Answer

    Solution

    Given, x 8  + x -8  = 194

    Or, {x 4  + (1/x 4 )} 2  – 2 = 194 (Since, (a + b) 2  = a 2  + b 2  + 2ab)

    Or, {x 4  + (1/x 4 )} = √(194 + 2)

    Or, {x 4  + (1/x 4 )} = 14

    Or, {x 2  + (1/x 2 )} 2  – 2 = 14 (Since, (a + b) 2  = a 2  + b 2  + 2ab)

    Or, {x 2  + (1/x 2 )} = √(14 + 2)

    Or, {x 2  + (1/x 2 )} = 4

    Or, (x 4  + 1) = 4x 2

    Or, x 4  – 4x 2  = -1

    Also, (2x 2  – 4) 2  – 1

    = 4x 4  – 16x 2  + 16 – 1

    = 4(x 4  – 4x 2 ) + 15

    = 4 × (-1) + 15 = 11

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