Solve the following system in real numbers: \begin{cases} \log_2(x+y)+4=2^x+2^y \\ \frac{x+y}{4}+\frac{xy}{x+y}=1 \end{cases}

I used the fact that $\frac{xy}{x+y} \leq \frac{x+y}{4}$ in order to get $x+y \geq 2$, but I couldn't find even one solution afterwards.

  • $\begingroup$ you can solve the second equation for $y$ or $x$ and you can plug the in the first equation $\endgroup$ – Dr. Sonnhard Graubner Mar 7 '17 at 19:20
  • $\begingroup$ i think a numerical method will help here $\endgroup$ – Dr. Sonnhard Graubner Mar 7 '17 at 19:21

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