Seemingly Random Polynomial

Algebra Level 4

x63+x44+x37+x31+x26+x9+6 \large x^{63} + x^{44} + x^{37} + x^{31} + x^{26} + x^9 + 6

If xx satisfies the equation (x+1x)2=3 \left(x + \dfrac1x\right)^2 = 3 , then find the value of the expression above.

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