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

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Answer 1 · 2018-06-01T10:02:24

$x=+-1$

Given curve is-
$y= x-1/x$

$dy/dx= 1+1/x^2$

$Slope= 1+1/x^2$

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

By giving condition,

$2= 1+1/x^2$

$1= 1/x^2$

$1=x^2$

$x=+-1$