Calculus in system of equations

Algebra Level 3

\(\begin{cases}x^2+y^2=145\\ x^3+y^3=1729 \end{cases}\\\)

If \((x_1,y_1),(x_2,y_2)...(x_n,y_n)\) are all the positive real ordered pairs which satisfy the system of equations above,then find value of\( x_1+x_2+...+x_n+y_1+...+y_n.\)

Note: Ordered pair means (1,2) and (2,1) are distinct

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