Ta có: \(\left(x+\sqrt{x^2+2023}\right)\left(y+\sqrt{y^2+2023}\right)=2023\)
=>\(\left(x-\sqrt{x^2+2023}\right)\left(x+\sqrt{x^2+2023}\right)\left(y+\sqrt{y^2+2023}\right)=2023\left(x-\sqrt{x^2+2023}\right)\)
=>\(\left(x^2-x^2-2023\right)\left(y+\sqrt{y^2+2023}\right)=2023\left(x-\sqrt{x^2+2023}\right)\)
=>\(y+\sqrt{y^2+2023}=-x+\sqrt{x^2+2023}\)
=>\(y+x+\sqrt{y^2+2023}-\sqrt{x^2+2023}=0\)
=>\(x+y+\frac{y^2+2023-x^2-2023}{\sqrt{y^2+2023}+\sqrt{x^2+2023}}=0\)
=>\(\left(x+y\right)+\frac{\left(y-x\right)\left(y+x\right)}{\sqrt{y^2+2023}+\sqrt{x^2+2023}}=0\)
=>\(\left(x+y\right)\left(1+\frac{y-x}{\sqrt{x^2+2023}+\sqrt{y^2+2023}}\right)=0\)
=>x+y=0
=>\(\left(x+y\right)^{2023}=0^{2023}=0\)
