Question

$x - \frac{1}{x} = 1$
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Answer 1

Respuesta:

$x - \frac{1}{x} = 1 \\ \frac{ {x}^{2} - 1}{x} = 1 \\ {x}^{2} - 1 = x \\ {x}^{2} - 1 - x = 0 \\ {x}^{2} - x - 1 \\ a = 1 \: b = - 1 \: c = - 1 \\ x = \frac{ - ( - 1) + - \sqrt{( { - 1}^{2} ) - 4 \times 1 \times - 1} }{2 \times 1} \\ x = \frac{1 + - \sqrt{1 + 4} }{2} \\ x = \frac{1 + - \sqrt{5} }{2} \\ x1 = \frac{1 + \sqrt{5} }{2} \\ x2 = \frac{1 - \sqrt{5} }{2}$