A weird system of equations.

Algebra Level 2

{x2+y2+z2=14x3+y3+z3=16\begin{cases} x^{2}+y^{2}+z^{2}=\frac{1}{4} \\\\ x^{3}+y^{3}+z^{3}=\frac{1}{6} \end{cases}

How many real solutions (x,y,z)(x, y, z) does the system above have?

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