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if x² + 1/x² = 18 Find the value of x - 1/x x + 1/x

$x^{2} + \frac{1}{x^{2}} = 18 x^{2} + \frac{1}{x^{2}} + 2 x (\frac{1}{x}) - 2 x (\frac{1}{x}) = 18 {(x - \frac{1}{x})}^{2} + 2 = 18 {(x - \frac{1}{x})}^{2} = 16 x - \frac{1}{x} = \pm 4 a n d x^{2} + \frac{1}{x^{2}} = 18 {(x + \frac{1}{x})}^{2} - 2 = 18 {(x + \frac{1}{x})}^{2} = 20 x + \frac{1}{x} = \pm \sqrt{20}$

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