Question

Tìm x,y,z thoả mãn

x+y+z+8=2\(\sqrt{x-1}\) +\(4\sqrt{y-2}\) \(+6\sqrt{z-3}\)

Answer 1

Lời giải:

\(x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)

\(\Leftrightarrow x+y+z+8-2\sqrt{x-1}-4\sqrt{y-2}-6\sqrt{z-3}=0\)

\(\Leftrightarrow (x-1)-2\sqrt{x-1}+1+(y-2)-4\sqrt{y-2}+4+(z-3)-6\sqrt{z-3}+9=0\)

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

Điều này xảy ra khi :

\(\left\{\begin{matrix} \sqrt{x-1}-1=0\rightarrow x=2\\ \sqrt{y-2}-2=0\rightarrow y=6\\ \sqrt{z-3}-3=0\rightarrow z=12\end{matrix}\right.\)