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      Question

      If (x² + 1/x2) = 4, which of the options

      below is a possible value of x² - 1/x2 ?
      A √3 Correct Answer Incorrect Answer
      B 2√2 Correct Answer Incorrect Answer
      C 2√3 Correct Answer Incorrect Answer
      D 3 Correct Answer Incorrect Answer

      Solution

      x² - 1/x² = (x + 1/x) (x - 1/x) ------ (i) Here, (x² + 1/x²) = 4 => x² + 1/x² + 2 = 6 => (x + 1/x)² = 6 => (x + 1/x) = {{{`sqrt(6)` }}} Putting these value in eqn (i) we get, => x² - 1/x² = {{{`sqrt(6)` }}} {{{`xx` }}} {{{`sqrt(2)` }}} => {{{`sqrt(12)` }}} = 2{{{`sqrt(3)` }}}

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