Question

Giải phương trình:

\(\sqrt{x-5}+\sqrt{y-2005}+\sqrt{z+2007}=\frac{1}{2}\left(x+y+z\right)\)

Answer 1

ĐKXĐ: ...

\(\Leftrightarrow2\sqrt{x-5}+2\sqrt{y-2005}+2\sqrt{z+2007}=x+y+z\)

\(\Leftrightarrow x-5-2\sqrt{x-5}+1+y-2005-2\sqrt{y-2005}+1+z+2007-2\sqrt{z-2007}+1=0\)

\(\Leftrightarrow\left(\sqrt{x-5}-1\right)^2+\left(\sqrt{y-2005}-1\right)^2+\left(\sqrt{z+2007}-1\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-5}-1=0\\\sqrt{y-2005}-1=0\\\sqrt{z+2007}-1=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=6\\y=2006\\z=-2006\end{matrix}\right.\)