Solve for x in terms of y $\displaystyle y=x+\frac{1}{x}$ It was so interesting, but after 30 minutes I gave up.
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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
Last edited by pacman; Sep 24th 2009 at 04:27 AM.
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
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