Solve for x in terms of y
It was so interesting, but after 30 minutes I gave up.
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Solve for x in terms of y
It was so interesting, but after 30 minutes I gave up.
http://www.mathhelpforum.com/math-he...bff81749-1.gif
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
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
thanks woodsmith, you have an eye of the eagle