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      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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