Question

solve and Please Explain!!​

Answer 1

$x - \frac{1}{x} = 3 \\ = > \frac{ {x}^{2} - 1 }{x} = 3 \\ = > {x}^{2} - 1 = 3x \\ = > {x}^{2} - 3x - 1 = 0 \\ a = 1 \: b = - 3 \: c = - 1 \\ by \: using \: quadratic \: formula \\ \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a} \\ = \frac{ - ( - 3) ± \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 1)} }{2 \times 1} \\ = \frac{3 ± \sqrt{9 + 4} }{2} \\ = \frac{3 ± \sqrt{13} }{2} \\ roots \: are \\ \frac{3 + \sqrt{13} }{2} \: \: \: \: \: \: \: \: \: \frac{3 - \sqrt{13} }{2}$