Question

\(\dfrac{x}{4}=\dfrac{y}{3};\dfrac{y}{2}=\dfrac{z}{7}và2x-3y-z=57\)

thank những ng giúp mik ❤ ☺

Answer 1

\(\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{21}\)Theo tc dãy tỉ số bằng nhau ta có 

\(\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{21}=\dfrac{2x-3y-z}{16-18-21}=\dfrac{57}{-23}\Rightarrow x=-\dfrac{456}{23};y=-\dfrac{342}{23};z=-\dfrac{1197}{23}\)

Answer 2

Ta có: \(\dfrac{x}{4}=\dfrac{y}{3};\dfrac{y}{2}=\dfrac{z}{7}\Rightarrow\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{21}\Rightarrow\dfrac{2x}{16}=\dfrac{3y}{18}=\dfrac{z}{21}\)

AD t/c DTSBN ,có:

\(\dfrac{2x}{16}=\dfrac{3y}{18}=\dfrac{z}{21}=\dfrac{2x-3y-z}{16-18-21}=-\dfrac{57}{23}\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{8}=-\dfrac{57}{23}\\\dfrac{y}{6}=-\dfrac{57}{23}\\\dfrac{z}{21}=-\dfrac{57}{23}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{456}{23}\\y=-\dfrac{342}{23}\\z=-\dfrac{1197}{23}\end{matrix}\right.\)

Answer 3

x/4=y/3

nên x/8=y/6

y/2=z/7

nên y/6=z/21

=>x/8=y/6=z/21

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

\(\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{21}=\dfrac{2x-3y-z}{2\cdot8-3\cdot6-21}=\dfrac{57}{-23}\)

Do đó: x=-456/23; y=-342/23; z=-1197/23