Giúp mình bài dãy tỉ số = nhau này ^.*

S

soicon_boy_9x

$3x=4y=6z \rightarrow \dfrac{x}{\dfrac{1}{3}}=\dfrac{y}{\dfrac{1}{4}}= \dfrac{z}{\dfrac{1}{6}}$
Đặt $\dfrac{x}{\dfrac{1}{3}}=\dfrac{y}{\dfrac{1}{4}}= \dfrac{z}{ \dfrac{1}{6} } =k \rightarrow x=\dfrac{1}{3}k \ \ y=\dfrac{1}{4}k \ \ z=\dfrac{1}{6}k$
Lắp vào đề bài ta được:
$2x+y-z=2.\dfrac{1}{3}k+\dfrac{1}{4}k-\dfrac{1}{6}k=k(2.\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{6})=k.\dfrac{3}{4}=9$
$\rightarrow k=9:\dfrac{3}{4}=12$
$\rightarrow$ $x=12.\dfrac{1}{3}=4 \\ y=12.\dfrac{1}{4}=3 \\ z=12.\dfrac{1}{6}=2$
 
T

thaonguyenkmhd

Ta có $3x=4y=6z \rightarrow \dfrac{3x}{12}=\dfrac{4y}{12}=\dfrac{6z}{12} \rightarrow \dfrac{x}{4}=\dfrac{y}{3}=\dfrac{z}{2}$

Theo tính chất dãy tỉ số bằng nhau \Rightarrow $\dfrac{x}{4}=\dfrac{y}{3}=\dfrac{z}{2}=\dfrac{2x+y-z}{2.4+3-2}=\dfrac{9}{9}=1$

\Rightarrow $x=4 \\ y=3 \\ z=2$
 
You must log in or register to reply here.
Top Bottom