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      Question

      If x2 = 15x + 1, then find the value of

      {x3 - (1/x3) }.
      A 3405 Correct Answer Incorrect Answer
      B 3420 Correct Answer Incorrect Answer
      C 3560 Correct Answer Incorrect Answer
      D 3340 Correct Answer Incorrect Answer

      Solution

      We have, x2 = 15x + 1Divide both sides by 'x', x = 15 + (1/x) so, (x - 1/x) = 15 Cubing both sides, (x - 1/x)3 = 153 Using, (a - b) 3 = a3 - b3 - 3ab(a - b) (x - 1/x)3 = x3 - (1/x)3 - 3(x - 1/x) 153 = x3 - (1/x)3 - 3 x 15 So, (x - 1/x)3 = 2275 + 45 = 3420

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