Lets get insane

Algebra Level 4

\[ \begin{cases}x^4+2x^3-y=-\frac{1}{4}+\sqrt{3}\\ y^4+2y^3-x=-\frac{1}{4}-\sqrt{3} \end{cases}\]

All the ordered pairs of real numbers that satisfy the system of equations above are \((x_1,y_1),(x_2,y_2),...(x_n,y_n)\). Find the value of \(x_1+x_2+...+x_n+y_1+...y_n\) correct upto two decimal places.

  • If you think there are infinite solutions then answer 777 and if you think no real solutions answer 666.
  • Ordered pair means (11,12),(12,11) are considered different.

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