Question

Tìm tất cả các số x ,y,z biết x/y+z+1=y/x+z+2=z/x+y-3=x+y+z

 

 

Answer 1

ta có\(\frac{x}{y+z+1}=\frac{y}{x+z+2}=\frac{z}{x+y-3}=\frac{x+y+z}{y+z+1+x+z+2+x+y-3}=\frac{1}{2}\)

\(\Rightarrow x+y+z=\frac{1}{2}\)

\(\Rightarrow\frac{x}{\frac{1}{2}-x+1}=\frac{1}{2};\frac{y}{\frac{1}{2}-y+2}=\frac{1}{2};\frac{z}{\frac{1}{2}-z-3}=\frac{1}{2}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{5}{6}\\z=-\frac{5}{6}\end{cases}}\)