# how to find all values of x for which the tangent to y=x-(1/x) is parallel to the line 2x-y=5?

Jun 1, 2018

$x = \pm 1$

#### Explanation:

Given curve is-
$y = x - \frac{1}{x}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 1 + \frac{1}{x} ^ 2$

$S l o p e = 1 + \frac{1}{x} ^ 2$

Slope of the line $2 x - y = 5$ is $2$

By giving condition,

$2 = 1 + \frac{1}{x} ^ 2$

$1 = \frac{1}{x} ^ 2$

$1 = {x}^{2}$

$x = \pm 1$