Question

Answer 1

<=>\(x+y+z-6000-2\sqrt{x-2000}-2\sqrt{y-2001}-\sqrt{z-2002}=0\)

<=>\(\left[\left(x-2000\right)-2\sqrt{x-2000}+1\right]+\left[\left(y-2001\right)-2\sqrt{y-2001}+1\right]+\left[\left(z-2002\right)-2\sqrt{z-2002}+1\right]=0\)<=>\(\left(\sqrt{x-2000}-1\right)^2+\left(\sqrt{y-2001}-1\right)^2+\left(\sqrt{z-2002}-1\right)^2=0\)

<=>\(\left\{{}\begin{matrix}x-2000=1\\y-2001=1\\z-2002=1\end{matrix}\right.\)=>\(\left\{{}\begin{matrix}x=2001\\y=2002\\z=2003\end{matrix}\right.\)