Question

Tìm x,y,z biết:

\(\dfrac{6}{11}\) x= \(\dfrac{7}{2}\) y=\(\dfrac{18}{5}\) z và -x+y+z=-120

Answer 1

\(\dfrac{6}{11}x=\dfrac{7}{2}y=\dfrac{18}{5}z\)

\(\Rightarrow\dfrac{6x}{11.126}=\dfrac{7y}{2.126}=\dfrac{18z}{5.126}\)

\(\Rightarrow\dfrac{x}{231}=\dfrac{y}{36}=\dfrac{z}{35}\)

Theo tính chất của dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{231}=\dfrac{y}{36}=\dfrac{z}{35}=\dfrac{-x+y+z}{-231+36+35}=\dfrac{-120}{-160}=\dfrac{3}{4}\)

\(\Rightarrow\dfrac{x}{231}=\dfrac{3}{4}\Rightarrow x=\dfrac{693}{4}\)

\(\dfrac{y}{36}=\dfrac{3}{4}\Rightarrow y=27\)

\(\dfrac{z}{35}=\dfrac{3}{4}\Rightarrow z=\dfrac{105}{4}\)