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      Question

      If a = (√2 - 1)1/3, then the value of

      (a-1/a)3 +3(a-1/a) is:
      A √2 Correct Answer Incorrect Answer
      B 2 Correct Answer Incorrect Answer
      C -2 Correct Answer Incorrect Answer
      D -√2 Correct Answer Incorrect Answer

      Solution

      a = (√2 - 1)1/3               both sides cube a3= (√2 - 1)     … (1) Now- (a-1/a)3 + 3(a-1/a)       using formula (a-b)3 =a3-b3-3ab(a-b) =a3-1/a3 -3×a×1/a(a-1/a) +3(a-1/a) = a3-1/a3 -3(a-1/a) + 3(a-1/a) = a3-1/a3 Now put the value of a3. = (√2 - 1) -1/ (√2 - 1) = (√2 - 1) – [(√2 + 1)/ (√2 - 1) (√2 + 1)] = (√2 - 1- √2 - 1) =-1-1 =-2.

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