System of equations

Algebra Level 4

\[ \begin{cases} {y = \sqrt { x+1 } +\sqrt [ 4 ]{ x-1 } -\sqrt { { y }^{ 4 }+2 } } \\ {0=x^2+2x(y-1)+y^2-6y+1} \end{cases} \]

Let \((x_1,y_1), (x_2,y_2), \ldots , (x_n,y_n)\) be the solution set of the above system of equations for real \(x,y\)

Evaluate \( \displaystyle n+ \sum _{ i=1 }^{ n }{ (x_i+y_i) } \)

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