Đáp án + giải thích các bước giải:
`(x+\sqrt{x^2+2013})(y+\sqrt{y^2+2013})=2013`
`->(x^2-(x^2+2013))/(x-\sqrt{x^2+2013}) . (y^2-(y^2+2013))/(y-\sqrt{y^2+2013})=2013`
`->2013^2/((x-\sqrt{x^2+2013})(y-\sqrt{y^2+2013}))=2013`
`->(x-\sqrt{x^2+2013})(y-\sqrt{y^2+2013})=2013`
`->(x-\sqrt{x^2+2013})(y-\sqrt{y^2+2013})=(x+\sqrt{x^2+2013})(y+\sqrt{y^2+2013})`
`->xy-y\sqrt{x^2+2013}-x\sqrt{y^2+2013}+\sqrt{(x^2+2013)(y^2+2013)}=xy+y\sqrt{x^2+2013}+x\sqrt{y^2+2013}+\sqrt{(x^2+2013)(y^2+2013)}`
`->-2x\sqrt{y^2+2013}=2y\sqrt{x^2+2013} `
`->-x\sqrt{y^2+2013}=y\sqrt{x^2+2013} (->x\ney)`
`->x^2y^2+2013x^2=y^2x^2+2013y^2`
`->x^2=y^2`
`->`\(\left[ \begin{array}{l}x=y(KTM)\\x=-y\end{array} \right.\)
`->x=-y`
`->x^2013=(-y)^2013=-y^2013`
`->x^2013+y^2013=-y^2013+y^2013=0`
`->đpcm`
