Calculate x-1x- when x4-1x4-727-

Given x^4+1x^4=727, x 1x=? We know that (x^2+1x^2)^2=x^4+1x^4+2.x^2. 1x^2 727+2=729 ∴ x^2+1x^2=√(7)29=27 again (x 1x)^2=x^2+1x^2 2.x.1x ...

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Rational Expression

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Question

Calculate $x - \frac{1}{x},$ when $x^{4} + \frac{1}{x^{4}} = 727$ .

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