# Math Help - Solving for x

1. ## Solving for x

Solve for x in terms of y

$y=x+\frac{1}{x}$

It was so interesting, but after 30 minutes I gave up.

2. ## y = x + 1/x

y = x + 1/x

xy = x^2 + 1

x^2 - xy + 1 = 0, quadratic in x,

x = [-(-y) +/- ((-y)^2 - 4(1)(1))^1/2]/2

x = [y (+/-) (y^2 - 4)^(1/2)]/2

positive root:

x = y/2 +[sqrt (y^ - 4)]/2

negative root;

x = y/2 -[sqrt (y^ - 4)]/2

plot below of y = x + 1/x

3. The above answer missed "2", it should be

positive root:

x = y/2 +[sqrt (y^2 - 4)]/2

negative root;

x = y/2 -[sqrt (y^ 2- 4)]/2

4. thanks woodsmith, you have an eye of the eagle