Question

The two values of x in the equation x - 1/x = 3 are ​

Answer 1

Step-by-step explanation:

$x - \frac{1}{x} = 3 \\ \\ \frac{ {x}^{2} - 1 }{x} = 3 \\ \\ \frac{ {x}^{2} - 1}{1} = 3x \\ \\ {x}^{2} - 3x - 1 = 0 \\ \\ discriminant = {b}^{2} - 4ac \\ \\ = {9}^{2} - 4(1)( - 1) \\ \\ = 81 + 4 \\ = 85 \\ \\ x = \frac{3 + \sqrt{85} }{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{3 - \sqrt{85} }{2}$