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      Question

      If [x + (1/x) ] = 4, then find the value of [x

      >3┬а+ (1/x 3) ].
      A 52 Correct Answer Incorrect Answer
      B 56 Correct Answer Incorrect Answer
      C 60 Correct Answer Incorrect Answer
      D 64 Correct Answer Incorrect Answer

      Solution

      x + (1/x) = 4 On squaring both sides, We get, [x + (1/x) ]2┬а= 42 Or, x2┬а+ (1/x2) + 2 = 16 Or, x2┬а+ (1/x2) = 14 ------- (I) Using a3┬а+ b3┬а= (a + b) (a2┬а+ b2┬а- ab) x3┬а+ (1/x3) = [x + (1/x) ][x2┬а+ (1/x2) - 1] = 4 X (14 - 1) (From equation I) = 4 X 13 = 52

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