Question

Tim x,y,z biet: \(\dfrac{1}{2}\left(x+y+z\right)-3=\sqrt{x-2}+\sqrt{y-3}+\sqrt{z-4}\)

Answer 1

ĐK : \(x\ge2,y\ge3,z\ge4\) .

\(pt\Leftrightarrow x+y+z-6=2\sqrt{x-2}+2\sqrt{y-3}+2\sqrt{z-4}\)

\(\Leftrightarrow\left[\left(x-2\right)-2\sqrt{x-2}+1\right]+\left[\left(y-3\right)-2\sqrt{y-3}+1\right]+\left[\left(z-4\right)-2\sqrt{z-4}+1\right]=0\)

\(\Leftrightarrow\left(\sqrt{x-2}-1\right)^2+\left(\sqrt{y-3}-1\right)^2+\left(\sqrt{z-4}-1\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=4\\z=5\end{matrix}\right.\left(TM\right)\)