Question

^{2x = 3y = 5z va x - y + z = -33 . Tim x,y,z}

 

Answer 1

\(2x=3y=5z\Rightarrow\frac{2x}{30}=\frac{3y}{30}=\frac{5z}{30}\Rightarrow\frac{x}{15}=\frac{y}{10}=\frac{z}{6}\)

\(\Rightarrow\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x-y+z}{15-10+6}=\frac{-33}{11}=-3\)

\(\Rightarrow\hept{\begin{cases}x=-3.15=-45\\y=-3.10=-30\\z=-3.6=-18\end{cases}}\)

Vậy \(x=-45\), \(y=-30\), \(z=-18\).

Answer 2

Ta có:

2x=3y=5z=>\(\frac{2x}{30}=\frac{3y}{30}=\frac{5y}{30}\)=>\(\frac{x}{15}=\frac{y}{10}=\frac{z}{6}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x-y+z}{15-10+6}=\frac{-33}{9}=\frac{-11}{3}\)

=>\(\frac{x}{15}=\frac{-11}{3}\)=>\(x=\frac{-11}{3}.15=-55\)

    \(\frac{y}{10}=\frac{-11}{3}\)=>\(y=\frac{-11}{3}.10=\frac{-110}{3}\)

     \(\frac{z}{6}=\frac{-11}{3}\)=>\(z=-\frac{11}{3}.6=-22\)

Vậy