Odd Powers Only

Algebra Level 4

m=02015(x2m+1+1x2m+1)2 \large \sum_{m=0}^{2015} \left( x^{2m+1} + \dfrac1{x^{2m+1}} \right)^2

If xx is a complex number such that it satisfies the constraint (x+1x)2=2 \left( x + \frac1x\right)^2 = 2, find the value of the summation above.

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