Question

Tìm các số x,y,z \(\in Q\) biết rằng ( x + y ) : ( 5 - z ) : ( y + z ) : ( 9 + y ) = 3 : 1 : 2 : 5

Answer 1

Ta có \(\frac{x+y}{3}=\frac{5-z}{1}=\frac{y+z}{2}=\frac{9+y}{5}=k\left(1\right)\)

\(\frac{\left(x+y\right)+\left(5-z\right)+\left(y+z\right)+\left(9+y\right)}{3+1+2+5}=\frac{x+y-4}{1}\)

\(\Rightarrow\left\{\begin{matrix}x+y-4=k\\x+y=3k\end{matrix}\right.\)\(\Rightarrow k+4=x+y\)

\(\Rightarrow4+k=3k\Rightarrow4=2k\Rightarrow k=2\)

\(\Rightarrow5-z=k\Rightarrow z=5-k=5-2=3\)

\(9+y=5k\Rightarrow y=5k-9=10-9=1\)

\(x+y=3k\Rightarrow x=3k-y=6-1=5\)

Từ \(\left(1\right)\Rightarrow\left\{\begin{matrix}x=5\\y=1\\z=3\end{matrix}\right.\)