# Finite or infinite number of roots!

Algebra Level 3

The equation $x^3=-1$ 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 $\large x^{\frac{1}{\sqrt{2}}}=-1$

Note: When $x$ is a complex number different from $0$, and $r$ is a real number, $x^r$ can have more than one possible value. In this case, we assume that the complex number $x$ is a solution of the equation $x^r=s,$ where $s$ is a given real number, if at least one of the values of $x^r$ is equal to $s.$

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