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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