Finite or infinite number of roots!

Algebra Level 4

The equation x3=1x^3=-1 has three solutions, one of which is real and the other two are non-real complex numbers. Determine the number and type of solutions of x12=1 \large x^{\frac{1}{\sqrt{2}}}=-1

Note: When xx is a complex number different from 00, and rr is a real number, xrx^r can have more than one possible value. In this case, we assume that the complex number xx is a solution of the equation xr=s,x^r=s, where ss is a given real number, if at least one of the values of xrx^r is equal to s.s.

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