# Some algebra

Algebra Level 3

$\large{ \begin{cases} x+y+z=1 \\ x^2+y^2+z^2=35 \\ x^3 + y^3 + z^3 = 97 \end{cases} }$

Let $$x,y$$ and $$z$$ satisfy the system of equations above. Find $$\max(x,y,z)$$.

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