Đáp án:
Giải thích các bước giải:
`\sqrt{x-2000}+\sqrt{y-2001}+\sqrt{z-2002}=1/2(x+y+z)-3000(ĐKXĐ:x>=2000;y>=20001;z>=2002)`
`<=>2\sqrt{x-2000}+2\sqrt{y-2001}+2\sqrt{z-2002}=x+y+z-6000`
`<=>x+y+z-6000-2\sqrt{x-2000}-2\sqrt{y-2001}-2\sqrt{z-2002}=0`
`<=>[(x-2000)-2\sqrt{x-2000}+1]+[(y-2001)-2\sqrt{y-2001}+1]+[(z-2002)-2\sqrt{z-2002}+1]=0`
`<=>(\sqrt{x-2000}-1)^2+(\sqrt{y-2001}-1)^2+(\sqrt{z-2002}-1)^2=0`
Vì `(\sqrt{x-2000}-1)^2+(\sqrt{y-2001}-1)^2+(\sqrt{z-2002}-1)^2>=0`
`=>`$\begin{cases}x-2000=1\\y-2001=1\\z-2002=1\end{cases}$
`=>`$\begin{cases}x=2001\\y=2002\\z=2003\end{cases}(tm)$
