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Suppose x3+1x3=52x^3+\dfrac{1}{x^3}=52x3+x31=52. What is the product of all distinct complex values of x+1xx+\dfrac{1}{x}x+x1?
Note that in this case, "complex" indicates the number is of the form a+bia+bia+bi where b≠0b\ne 0b=0.
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