What is \left(x^2 + \frac{1}{x^2}\right) equal to ?

Explanation

The equation is x^4 + \frac{1}{x^4} = \frac{257}{16}. Adding 2 to both sides gives \left(x^2 + \frac{1}{x^2}\right)^2 = \frac{257}{16} + \frac{32}{16} = \frac{289}{16}. Taking the positive square root gives \frac{17}{4}.

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