Ta có:\(\left(x+\sqrt{x^2+2015}\right)\left(y-\sqrt{y^2+2015}\right)\left(y+\sqrt{y^2+2015}\right)=2015\left(y-\sqrt{y^2+2015}\right)\)
\(\Leftrightarrow-2015\left(x+\sqrt{x^2+2015}\right)=2015\left(y-\sqrt{y^2+2015}\right)\)
\(\Leftrightarrow x+\sqrt{x^2+2015}=\sqrt{y^2+2015}-y\) (1)
Lại có:\(\left(x+\sqrt{x^2+2015}\right)\left(x-\sqrt{x^2+2015}\right)\left(y+\sqrt{y^2+2015}\right)=2015\left(x-\sqrt{x^2+2015}\right)\)
\(\Leftrightarrow-2015\left(y+\sqrt{y^2+2015}\right)=2015\left(x-\sqrt{x^2+2015}\right)\)
\(\Leftrightarrow y+\sqrt{y^2+2015}=\sqrt{x^2+2015}-x\) (2)
Cộng theo vế \(\left(1\right)\) và \(\left(2\right)\) ta có:\(x+\sqrt{x^2+2015}+y+\sqrt{y^2+2015}=\sqrt{y^2+2015}+\sqrt{x^2+2015}-x-y\)
\(\Leftrightarrow2x+2y=0\Leftrightarrow x+y=0\)
