\(\left(x+\sqrt{x^2+2022}\right)\left(y+\sqrt{y^2+2022}\right)=2022\)
\(\Leftrightarrow\left(\sqrt{x^2+2022}-x\right)\left(x+\sqrt{x^2+2022}\right)\left(y+\sqrt{y^2+2022}\right)=2022\left(\sqrt{x^2+2022}-x\right)\)
\(\Leftrightarrow2022\left(y+\sqrt{y^2+2022}\right)=2022\left(\sqrt{x^2+2022}-x\right)\)
\(\Leftrightarrow y+\sqrt{y^2+2022}=\sqrt{x^2+2022}-x\) (1)
Tương tự ta có:
\(x+\sqrt{x^2+2022}=\sqrt{y^2+2022}-y\) (2)
Cộng vế (1) và (2):
\(\Rightarrow x+y+\sqrt{y^2+2022}+\sqrt{x^2+2022}=\sqrt{x^2+2022}+\sqrt{y^2+2022}-x-y\)
\(\Leftrightarrow2\left(x+y\right)=0\)
\(\Leftrightarrow x+y=0\)
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