a) Ta có: \(\dfrac{x}{y}=\dfrac{7}{20}\Rightarrow\dfrac{x}{7}=\dfrac{y}{20}\)

\(\dfrac{y}{z}=\dfrac{5}{8}\Rightarrow\dfrac{y}{5}=\dfrac{z}{8}\Rightarrow\dfrac{y}{20}=\dfrac{z}{32}\)

\(\Rightarrow\dfrac{x}{7}=\dfrac{y}{20}=\dfrac{z}{32}\)

\(\Rightarrow\dfrac{2x}{14}=\dfrac{5y}{100}=\dfrac{2z}{64}\)

Áp dụng tc dãy tỉ số bằng nhau:

\(\dfrac{2x}{14}=\dfrac{5y}{100}=\dfrac{2z}{64}=\dfrac{2x+5y-2z}{14+100-64}=2\)

Do \(\left\{{}\begin{matrix}\dfrac{2x}{14}=2\\\dfrac{5y}{100}=2\\\dfrac{2z}{64}=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=14\\y=40\\z=64\end{matrix}\right.\).

b) \(5x=8y=20z\Rightarrow\dfrac{5x}{40}=\dfrac{8y}{40}=\dfrac{20z}{40}\)

\(\Rightarrow\dfrac{x}{8}=\dfrac{y}{5}=\dfrac{z}{2}\)

Áp dụng...

\(\dfrac{x}{8}=\dfrac{y}{5}=\dfrac{z}{2}=\dfrac{x-y-z}{8-5-2}=3\)

....

c) \(\dfrac{6}{11}x=\dfrac{9}{2}y=\dfrac{18}{5}z\Rightarrow\dfrac{x}{\dfrac{11}{6}}=\dfrac{y}{\dfrac{2}{9}}=\dfrac{z}{\dfrac{5}{18}}\)

...

5x = 8y = 20z suy ra 5x/40 = 8y/40 = 20z/40 suy ra x/8 = y/5 = z/2 . ap dung tinh chat day ty so bang nhau ta co x/8 =y/5 =z/2 =          x-y-z/8-5-2 =3 /1 =3 . tu x/8 =3 suy ra x =24 . tu y /6=3 suy ra y=18 . tu z/2 =3 suy ra z =6 . vay x = 24 , y = 18 , z = 6

\(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\Rightarrow\frac{6x}{11.18}=\frac{9y}{2.18}=\frac{18z}{5.18}\)

\(\Rightarrow\frac{-x}{-33}=\frac{y}{4}=\frac{z}{5}=\frac{-x+y+z}{-33+4+5}=\frac{-120}{-24}=5\)

\(\Rightarrow x=165;y=20;z=25\)

\(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\Rightarrow\frac{6x}{11.18}=\frac{9y}{2.18}=\frac{18z}{5.18}\)

\(\Rightarrow\frac{-x}{-33}=\frac{y}{4}=\frac{z}{5}=\frac{-x+y+z}{-33+4+5}=\frac{-120}{-24}=5\)

\(\Rightarrow x=165;y=20;z=25\)

a) 5x = 8y = 20z => \(\dfrac{5x}{40}\)= \(\dfrac{8y}{40}\)=\(\dfrac{20z}{40}\)=> \(\dfrac{x}{8}=\dfrac{y}{5}=\dfrac{z}{2}\)

áp dụng tính chất dãy tỉ số = nhau . Và x-y-z=3 .Ta có

\(\dfrac{x}{8}=\dfrac{y}{5}=\dfrac{z}{2}\) =\(\dfrac{x-y-z}{8-5-2}\)=3

\(\dfrac{x}{8}\)=3 => x= 8.3

=> x = 24

\(\dfrac{y}{5}=3\)=> x = 5.3

=> x = 15

\(\dfrac{z}{2}\)=3 => x = 2.3

=> x =6

b ) (\(\dfrac{6}{11}\))x = (\(\dfrac{9}{2}\))y

---> x = (\(\dfrac{9}{2}\))(\(\dfrac{11}{6}\))y = (\(\dfrac{33}{4}\))y
(\(\dfrac{9}{2}\))y = (\(\dfrac{18}{5}\))z

---> z = (\(\dfrac{9}{2}\))(\(\dfrac{5}{18}\))y = (\(\dfrac{5}{4}\))y
---> - x + y + z = (\(\dfrac{-33}{4}\))y + y + (\(\dfrac{5}{4}\))y = - 120
---> - 6y = - 120 ---> y = 20 ---> x = 165 và z = 25.

a) \(\dfrac{x}{y}=\dfrac{9}{7}\)⇒\(\dfrac{x}{9}=\dfrac{y}{7}\)

\(\dfrac{y}{z}=\dfrac{7}{3}\)⇒\(\dfrac{y}{7}=\dfrac{z}{3}\)

⇒\(\dfrac{x}{9}=\dfrac{y}{7}=\dfrac{z}{3}\)

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

\(\dfrac{x}{9}=\dfrac{y}{7}=\dfrac{z}{3}=\dfrac{x-y+z}{9-7+3}=-\dfrac{15}{5}=-3\)

⇒\(\left\{{}\begin{matrix}x=-3.9=-27\\y=-3.7=-21\\z=-3.3=-9\end{matrix}\right.\)

c: Ta có: 5x=8y=20z

nên \(\dfrac{x}{\dfrac{1}{5}}=\dfrac{y}{\dfrac{1}{8}}=\dfrac{z}{\dfrac{1}{20}}\)

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

\(\dfrac{x}{\dfrac{1}{5}}=\dfrac{y}{\dfrac{1}{8}}=\dfrac{z}{\dfrac{1}{20}}=\dfrac{x-y-z}{\dfrac{1}{5}-\dfrac{1}{8}-\dfrac{1}{20}}=\dfrac{3}{\dfrac{1}{40}}=120\)

Do đó: x=24; y=15; z=6

a, 5x = 8y => \(\frac{x}{8}=\frac{y}{5}\)

8y = 20z => 2y = 5z => \(\frac{y}{5}=\frac{z}{2}\)

=> \(\frac{x}{8}=\frac{y}{5}=\frac{z}{2}\)

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

\(\frac{x}{8}=\frac{y}{5}=\frac{z}{2}=\frac{x-y-z}{8-5-2}=\frac{3}{1}=3\)

=> x = 24,y = 15,z = 6

b, \(\frac{6}{11}x=\frac{9}{2}y\)=> \(\frac{12x}{22}=\frac{99y}{22}\)=> 12x = 99y => 4x = 33y => \(\frac{x}{33}=\frac{y}{4}\)

\(\frac{9}{2}y=\frac{18}{5}z\)=> \(\frac{45y}{10}=\frac{36z}{10}\)=> 45y = 36z => 5y = 4z => \(\frac{y}{4}=\frac{z}{5}\)

=> \(\frac{x}{33}=\frac{y}{4}=\frac{z}{5}\)

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

\(\frac{x}{33}=\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{-x}{-33}=\frac{y}{4}=\frac{z}{5}=\frac{-x+y+z}{-33+4+5}=\frac{120}{-24}=-5\)

=> x = -165 , y = -20 , z = -25

c, Đặt : \(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}=k\)=> x = 12k , y = 9k , z = 5k

=> xyz = 12k . 9k . 5k

=> xyz = 540k³

=> 540k³ =20

=> k³ = 20/540

=> k³ = 1/27

=> k = 1/3

Do đó : x= 4 , y = 3 , z = 5/3

\(\frac{x}{4}=\frac{y}{3}=\frac{z}{9}=\)\(\frac{x}{4}=\frac{3y}{9}=\frac{4z}{36}\)

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

\(\frac{x}{4}=\frac{3y}{9}=\frac{4z}{36}=\frac{x-3y+4z}{4-9+36}=\frac{62}{31}=2\)

\(\frac{x}{4}=2=>x=8\)

\(\frac{3y}{9}=2=>y=6\)

\(\frac{4z}{36}=2=>z=18\)

Ta có: a) \(\hept{\begin{cases}\frac{x}{4}=\frac{y}{3}=\frac{z}{9}\\x-3y+4x=62\end{cases}\Rightarrow\frac{x-3y+4z}{4-9+36}=\frac{62}{31}=2}\)

\(\Rightarrow\hept{\begin{cases}x=2.4=8\\y=2.3=6\\z=2.9=18\end{cases}}\)

a) Ta có: x/4=y/3=z/9=x-3y+4z/4-9+36=62/31=2

 x/4=2 => x=2.4=8

 y/3=2 => y=2.3=6

 z/9=2 => z=2.9=18

Vậy x=8; y=6; z=18.

bài 3:

a, đặt \(\dfrac{x}{12}=\dfrac{y}{9}=\dfrac{z}{5}=k\)

=>x=12k,y=9k,z=5k

ta có: ayz=20=> 12k.9k.5k=20

=> (12.9.5)k^3=20

=>540.k^3=20

=>k^3=20/540=1/27

=>k=1/3

=>x=12.1/3=4

y=9.1/3=3

z=5.1/3=5/3

vậy x=4,y=3,z=5/3

b,ta có: \(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{3}=\dfrac{x^2}{25}=\dfrac{y^2}{49}=\dfrac{z^2}{9}\)

A/D tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{3}=\dfrac{x^2}{25}=\dfrac{y^2}{49}=\dfrac{z^2}{9}=\dfrac{x^2+y^2-z^2}{25+49-9}=\dfrac{585}{65}=9\)

=>x=5.9=45

y=7.9=63

z=3*9=27

vậy x=45,y=63,z=27

Theo mình thì bạn nên đăng từng câu hỏi chứ đăng 1 lượt thế này có 1 số bạn thấy dài quá ko mún làm và mình cũng ở trong số đó.

Dài quá biết làm mà làm mệt lắm!!!thông cảm!!!