First degree is equal to second degree?

Algebra Level pending

x+1x=x2+1x2\large x+ \frac{1}{x} = x^2 + \frac{1}{x^2}

If the equation above is true for some real positive value xx, what is the value of x1024+1x1024x^{1024} + \dfrac{1}{x^{1024}} ?

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