Question

Tìm x y z bt:\(\sqrt{x+1}\)+\(\sqrt{y-3}\)+\(\sqrt{z-1}\)=\(\frac{1}{2}\)(x+y+z)

Answer 1

ĐKXĐ: ...

\(\Leftrightarrow x+y+z=2\sqrt{x+1}+2\sqrt{y-3}+2\sqrt{z-1}\)

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+1}-1=0\\\sqrt{y-3}-1=0\\\sqrt{z-1}-1=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=0\\y=4\\z=2\end{matrix}\right.\)