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This question recently came up in a competitive exam and I have been struggling to find out the easiest way to solve it.

Given that $x = 2+3\sqrt{3}$, what is the value of $x^4 + 1/x^4$.

Could someone provide me with an approach other than the direct approach of multiplying $x$ to itself $4$ times and adding it to its reciprocal.

Thanks in advance!

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