\[\begin{eqnarray} x = 1 + \dfrac{1}{2 + \dfrac{1}{1+ \dfrac{1}{2+ \ddots}}} \end{eqnarray} \]

Find \( \left( 4x^{2} - 4 \right)^2 + \left(8x^{3} - 10 \right)^4 \).

**Note:** Can you do this without algebra manipulation?

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