Question

How do I solve this?​

Answer 1

`x = (3)/(2) + ( √(5) )/(2) ; \: \: x = (3)/(2) - ( √(5) )/(2)`

Explanation:

`1 + \frac{1}{ {x}^(2) } = (3)/(x) \\ \\ \frac{ {x}^(2) + 1 }{ {x}^(2) } = (3)/(x) \\ \\ {x}^(2) + 1 = \frac{3 {x}^(2) }{x} \\ \\ {x}^(2) + 1 = 3x \\ \\ {x}^(2) - 3x + 1 = 0 \\ equating \: it \: with \\ a {x}^(2) + bx + c = 0 \\ a = 1 \\ b = - 3 \\ c = 1 \\ \\ x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac} }{2a} \\ \\ x = \frac{ - ( - 3) \pm \sqrt{ {( - 3)}^(2) - 4 * 1 * 1} }{2 * 1} \\ \\ x = \frac{ 3 \pm \sqrt{ {9 - 4}} }{2} \\ \\ x = \frac{ 3 \pm \sqrt{ {5}} }{2} \\ \\ x = (3)/(2) + ( √(5) )/(2) ; \: \: x = (3)/(2) - ( √(5) )/(2)`