Question

Tìm các bộ số thực (x, y, z) thỏa mãn:

\(\sqrt{x-29}+2\sqrt{y-6}+3\sqrt{z-2011}+1016=\frac{1}{2}\left(x+y+z\right)\)

Answer 1

ĐKXĐ: ....

\(\Leftrightarrow2\sqrt{x-29}+4\sqrt{y-6}+6\sqrt{z-2011}+2032=x+y+z\)

\(\Leftrightarrow x-29-2\sqrt{x-29}+1+y-6-4\sqrt{y-6}+4+z-2011-6\sqrt{z-2011}+9=0\)

\(\Leftrightarrow\left(\sqrt{x-29}-1\right)^2+\left(\sqrt{y-6}-2\right)^2+\left(\sqrt{z-2011}-3\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-29}-1=0\\\sqrt{y-6}-2=0\\\sqrt{z-2011}-3=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=30\\y=10\\z=2020\end{matrix}\right.\)