Question

cho(x+\(\sqrt{x^2+\sqrt{2010}}\))(y+\(\sqrt{y^2+\sqrt{2010}}\))=\(\sqrt{2010}\) .Hãy tính tổng S=x\(^3\)+y\(^3\)

Answer 1

Ta có:

\(\left[x+\sqrt{\left(x+2010\right)}\right].\left[\sqrt{\left(x+2010\right)-x}\right]=2010\)

\(\Rightarrow\sqrt{\left(x-2010\right)-x}=\sqrt{\left(x+2010\right)+y}\left(1\right)\)

\(\Leftrightarrow\sqrt{\left(y+2010\right)-y}=\sqrt{\left(x+2010\right)+x}\left(2\right)\)

Công 2 vé lại với nhau, ta có:

\(\Rightarrow\sqrt{\left(x+2010\right)}+\sqrt{\left(y+2010\right)}-x-y=\sqrt{\left(x+2010\right)}+\sqrt{\left(y+2010\right)}+x+y\)

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

\(\Rightarrow x^3+y^3=0\)

Answer 2

Bạn làm sai đề rồi