Question

[ngothithuyhien]

Cho \(\left(x+\sqrt{x^2+2015}\right)\left(y+\sqrt{y^2+2015}\right)=2015\)

Tính x+y

Answer 1

[Witch Rose]

\(\left(x+\sqrt{x^2+2015}\right)\left(y+\sqrt{y^2+2015}\right)=2015\)

\(\Leftrightarrow\frac{2015}{\sqrt{x^2+2015}-x}\left(y+\sqrt{y^2+2015}\right)=2015\)

\(\Leftrightarrow\sqrt{x^2+2015}-x=y+\sqrt{y^2+2015}\left(1\right)\)

Tương tự : \(x+\sqrt{x^2+2015}=\sqrt{y^2+2015}-y\left(2\right)\)

(1)+(2):

\(x+\sqrt{x^2+2015}+y+\sqrt{y^2+2015}=\sqrt{x^2+2015}+\sqrt{y^2+2015}-x-y\)

\(\Leftrightarrow2\left(x+y\right)=0\Leftrightarrow x+y=0\)