Sai đề kìa \(x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
\(\Leftrightarrow x+y+z+8-2\sqrt{x-1}-4\sqrt{y-2}-6\sqrt{z-3}=0\)
\(\Leftrightarrow\left(x-2\sqrt{x-1}+1-1\right)+\left(y-4\sqrt{y-2}+4-2\right)+\left(z-6\sqrt{z-3}+9-3\right)=0\)
\(\Leftrightarrow\left(\sqrt{x-1}-1\right)^2+\left(\sqrt{y-2}-2\right)^2+\left(\sqrt{z-3}-3\right)^2=0\)
\(\Rightarrow\hept{\begin{cases}\sqrt{x-1}-1=0\\\sqrt{y-2}-2=0\\\sqrt{z-3}-3=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}\sqrt{x-1}=1\\\sqrt{y-2}=2\\\sqrt{z-3}=3\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=2\\y=6\\z=12\end{cases}}\)
Sai đề kìa x+y+z+8=2√x−1+4√y−2+6√z−3
⇔x+y+z+8−2√x−1−4√y−2−6√z−3=0
⇔(x−2√x−1+1−1)+(y−4√y−2+4−2)+(z−6√z−3+9−3)=0
⇔(√x−1−1)2+(√y−2−2)2+(√z−3−3)2=0
⇒{
| √x−1−1=0 |
| √y−2−2=0 |
| √z−3−3=0 |
⇒{
| √x−1=1 |
| √y−2=2 |
| √z−3=3 |