Bài 7:
2: \(\left(x+\sqrt{x^2+2018}\right)\left(y+\sqrt{y^2+2018}\right)=2018\)
=>\(\left(\sqrt{x^2+2018}+x\right)\left(\sqrt{y^2+2018}+y\right)\left(\sqrt{y^2+2018}-y\right)=2018\left(\sqrt{y^2+2018}-y\right)\)
=>\(\left(y^2+2018-y^2\right)\left(\sqrt{x^2+2018}+x\right)=2018\left(\sqrt{y^2+2018}-y\right)\)
=>\(2018\left(\sqrt{x^2+2018}+x\right)=2018\left(\sqrt{y^2+2018}-y\right)\)
=>\(\sqrt{x^2+2018}+x=\sqrt{y^2+2018}-y\)
=>\(\sqrt{x^2+2018}-\sqrt{y^2+2018}+x+y=0\)
=>\(\frac{x^2+2018-y^2-2018}{\sqrt{x^2+2018}+\sqrt{y^2+2018}}+\left(x+y\right)=0\)
=>\(\frac{\left(x-y\right)\left(x+y\right)}{\sqrt{x^2+2018}+\sqrt{y^2+2018}}+\left(x+y\right)=0\)
=>x+y=0
=>x=-y
\(A=x^{2018}-y^{2018}\)
\(=x^{2018}-\left(-x\right)^{2018}=0\)
