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Define

                    \(\textcolor{blue}{f(x) = \frac{1}{x + \frac{1}{x}}}\)

and

                    \(\textcolor{green}{g(x) = \frac{1}{x - \frac{1}{x}}}\)

Find the square of the largest real solution to the equation

                                                                                                    \(\textcolor{purple}{ (g(x))^2 - (f(x))^2 = \tfrac54}\)

 Dec 1, 2019
 #1
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The square of the largest real solution is 3/2.

 Dec 3, 2019

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