A child's play

Algebra Level 4

\[\dfrac{x^{80}+2x^{64}+2x^{56}+x^{48}+4x^{40}+x^{32}+2x^{24}+2x^{16}+1}{x^{40}}\]

Given that \(x+\dfrac{1}{x}=\sqrt{3}\), find the value of the expression above.


This problem is original.
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