Question

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

tính P=x+y

Answer 1

Nhân liên hợp zô :v

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

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

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

Tương tự, ta cũng suy ra:

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

Cộng vế theo vế ta được x+y=0

Ahihi :v

Answer 2

=0