What is one of the possible values of x^{2}+\frac{1}{x^{2}}?

Explanation

From the previous solution, we have y = x - \frac{1}{x} = \frac{8}{3} (or \frac{3}{2}). We know x^2 + \frac{1}{x^2} = y^2 + 2. Using y = \frac{8}{3}, we get (\frac{8}{3})^2 + 2 = \frac{64}{9} + \frac{18}{9} = \frac{82}{9}.

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