How am I supposed to do that?

Algebra Level 5

Solve the following system for real \(x\) and \(y\) \[5x\left ( 1+\dfrac{1}{x^2+y^2}\right )=12\] \[5y\left ( 1-\dfrac{1}{x^2+y^2}\right )=4\]


Note

  • Enter your answer as the sum of all such values of \(x\) and \(y\).
  • This question once appeared in RMO.
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