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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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