\(\dfrac{5z-6y}{4}=\dfrac{6x-4z}{5}=\dfrac{4y-5x}{6}\)

\(\Rightarrow\dfrac{5z-6y}{4}=\dfrac{6x-4z}{5}=\dfrac{4y-5x}{6}=\dfrac{5z-6y+6x-4z+4y-5x}{4+5+6}=\dfrac{x-2y+z}{4+5+6}\)

\(\Rightarrow\dfrac{x}{4}=\dfrac{-2y}{5}=\dfrac{z}{6}\)

\(\Rightarrow\dfrac{3x}{12}=\dfrac{-2y}{5}=\dfrac{5z}{30}\)

\(\Rightarrow\dfrac{3x}{12}=\dfrac{-2y}{5}=\dfrac{5z}{30}=\dfrac{3x-2y+5z}{12-5+30}=\dfrac{96}{37}\)

a) \(\dfrac{x^3}{8}=\dfrac{y^3}{64}=\dfrac{z^3}{216}\)

Từ \(\dfrac{x^3}{8}=\dfrac{y^3}{64}=\dfrac{z^3}{216}\Rightarrow\dfrac{x^3}{2^3}=\dfrac{y^3}{4^3}=\dfrac{z^3}{6^3}\)

\(\Leftrightarrow\dfrac{x^2}{2^2}=\dfrac{y^2}{4^2}=\dfrac{z^2}{6^2}\Leftrightarrow\dfrac{x^2}{4}=\dfrac{y^2}{16}=\dfrac{z^2}{36}\)

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

\(\dfrac{x^2}{4}=\dfrac{y^2}{16}=\dfrac{z^2}{36}=\dfrac{x^2+y^2+z^2}{4+16+36}=\dfrac{14}{56}=\dfrac{1}{4}\)

\(\Rightarrow\dfrac{x^2}{4}=\dfrac{1}{4}\Rightarrow x^2=\dfrac{1}{4}\cdot4\Rightarrow x^2=1\Rightarrow x=1\)

\(\dfrac{y^2}{16}=\dfrac{1}{4}\Rightarrow y^2=\dfrac{1}{4}\cdot16\Rightarrow y^2=4\Rightarrow y=2\)

\(\dfrac{z^2}{36}=\dfrac{1}{4}\Rightarrow z^2=\dfrac{1}{4}\cdot36\Rightarrow z^2=9\Rightarrow z^2=3\)

Xin lỗi mình chỉ làm được câu a)

Ta có : \(\frac{5z-6y}{4}=\frac{6x-4z}{5}=\)\(\frac{4y-5x}{6}\)\(=\frac{20z-24y}{16}=\frac{30x-20z}{25}=\frac{24y-30x}{36}\)

\(=\frac{20z-24y+30x-20z+24y-30x}{16+25+36}\)\(=0\)

\(\Rightarrow\frac{5z-6y}{4}=0\Leftrightarrow5z-6y=0\Leftrightarrow5z=6y\Leftrightarrow\frac{y}{5}=\frac{z}{6}\left(1\right)\)

\(\Rightarrow\frac{6x-4z}{5}=0\Leftrightarrow6x-4z=0\Leftrightarrow6x=4z\Leftrightarrow\frac{z}{6}=\frac{x}{4}\left(2\right)\)

Từ \(\left(1\right);\left(2\right)\Rightarrow\)\(\frac{y}{5}=\frac{z}{6}=\frac{x}{4}\)\(=\frac{3x}{12}=\frac{2y}{10}=\frac{5z}{30}\)

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

\(\frac{3x}{12}=\frac{2y}{10}=\frac{5z}{30}=\frac{3x-2y+5z}{12-10+30}=\frac{96}{32}=3\)

\(\Rightarrow\frac{x}{4}=3\Leftrightarrow x=3.4=12\)

\(\Rightarrow\frac{y}{5}=3\Leftrightarrow y=3.5=15\)

\(\Rightarrow\frac{z}{6}=3\Leftrightarrow z=3.6=18\)

Vậy \(\hept{\begin{cases}x=12\\y=15\\z=18\end{cases}}\)

       Bài làm :

Ta có :

 \(\frac{5z-6y}{4}=\frac{6x-4z}{5}=\frac{4y-5x}{6}=\frac{20z-24y}{16}=\frac{30x-20z}{25}=\frac{24y-30x}{36}\)\(\)

\(=\frac{20z-24y+30x-20z+24y-30x}{16+25+36}\)

\(=0\)

\(\Rightarrow\frac{5z-6y}{4}=0\Leftrightarrow5z-6y=0\Leftrightarrow5z=6y\Leftrightarrow\frac{y}{5}=\frac{z}{6}\left(1\right)\)

\(\Rightarrow\frac{6x-4z}{5}=0\Leftrightarrow6x-4z=0\Leftrightarrow6x=4z\Leftrightarrow\frac{z}{6}=\frac{x}{4}\left(2\right)\)

Từ (1) và (2)

\(\Rightarrow\frac{y}{5}=\frac{z}{6}=\frac{x}{4}=\frac{3x}{12}=\frac{2y}{10}=\frac{5z}{30}\)

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

\(\frac{3x}{12}=\frac{2y}{10}=\frac{5z}{30}=\frac{3x-2y+5z}{12-10+30}=\frac{96}{32}=3\)

\(\Rightarrow\frac{x}{4}=3\Leftrightarrow x=3.4=12\)

\(\Rightarrow\frac{y}{5}=3\Leftrightarrow y=3.5=15\)

\(\Rightarrow\frac{z}{6}=3\Leftrightarrow z=3.6=18\)

Vậy x=12 ; y=15 ; z=18

Con tham khảo bài tương tự tại đây nhé:

Câu hỏi của ngoc Ngoc - Toán lớp 7 - Học toán với OnlineMath

\(\frac{5z-6y}{4}\)=\(\frac{6x-4y}{5}=\frac{4y-5x}{6}=\frac{20z-24y}{16}=\frac{30x-20z}{25}=\frac{24y-30x}{36}\)

=\(\frac{20z-24y+30x-20z+24y-30x}{16+25+36}=\frac{0}{77}=0\)

=>\(\frac{5z-6y}{4}=0=>5z-6y=0=>5z=6y=>\frac{y}{5}=\frac{z}{6}\left(1\right)\)

Tương tự ta có:\(\frac{x}{4}=\frac{y}{5}=\frac{z}{6}=\frac{3x}{12}=\frac{2y}{10}=\frac{5z}{30}\)

*Áp dụng dãy tỉ số bằng nhau ta có:

\(\frac{3z}{12}=\frac{2y}{10}=\frac{5z}{30}=\frac{3z-2y+5z}{12-10+30}=\frac{96}{32}=3\)

Tự giải nhé Đô Long

                                                              Kí tên: BTS V

\(\dfrac{5z-6y}{4}=\dfrac{6x-4z}{5}=\dfrac{4y-5x}{6}\)

\(\Leftrightarrow\dfrac{4\left(5z-6y\right)}{16}=\dfrac{5\left(6x-4z\right)}{25}=\dfrac{6\left(4y-5x\right)}{36}\)

\(\Leftrightarrow\dfrac{20z-24y}{16}=\dfrac{30x-20z}{25}=\dfrac{24y-30x}{36}\)

ADTCDTSBN có:

\(\dfrac{20z-24y}{16}=\dfrac{30x-20z}{25}=\dfrac{24y-30x}{36}=\dfrac{20z-24y+30x-20z+24y-30x}{16+25+36}=0\)

Do đó \(20z-24y=0;30x-20z=0\)

\(\Leftrightarrow5z=6y;6x=4z\)

\(\Rightarrow y=\dfrac{5z}{6};x=\dfrac{4z}{6}\)

Có \(3x-3y+5z=96\Rightarrow3.\dfrac{4z}{6}-3.\dfrac{5z}{6}+5z=96\)

\(\Rightarrow z=\dfrac{64}{3}\) \(\Rightarrow y=\dfrac{160}{9}\)và \(x=\dfrac{128}{9}\)

Vậy...

cho x/3 = y/4 và y/5 = z/6. tìm M = 2x + 3y+ 4z / 3x + 4y + 5z

Vi 8x = 5y , 7y = 12z

=>\(\left\{{}\begin{matrix}\dfrac{x}{5}=\dfrac{y}{8}\\\dfrac{y}{12}=\dfrac{z}{7}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{x}{60}=\dfrac{y}{96}\\\dfrac{y}{96}=\dfrac{z}{56}\end{matrix}\right.\)

=> \(\dfrac{x}{60}=\dfrac{y}{96}=\dfrac{z}{56}\)
Ap dung tinh chat day ti so bang nhau co
\(\dfrac{x}{60}=\dfrac{y}{96}=\dfrac{z}{56}=\dfrac{x+y+z}{60+96+56}=\dfrac{-318}{212}=\dfrac{-3}{2}\)
\(\dfrac{x}{60}=\dfrac{-3}{2}\Rightarrow x=60.\dfrac{-3}{2}=-90\)
\(\dfrac{y}{96}=\dfrac{-3}{2}\Rightarrow y=96.\dfrac{-3}{2}=-144\)
\(\dfrac{z}{56}=\dfrac{-3}{2}\Rightarrow z=56.\dfrac{-3}{2}=-84\)
Vay x= -90, y= -144 va z=-84

c: =>|x-2009|=2009-x

=>x-2009<=0

=>x<=2009

d: =>2x-1=0 và y-2/5=0 và x+y-z=0

=>x=1/2 và y=2/5 và z=x+y=1/2+2/5=9/10

a: 8x=5y; 7y=12z

=>x/5=y/8; y/12=z/7

=>x/15=y/24=z/14

Áp dụng tính chất của DTSBN, ta được:

\(\dfrac{x}{15}=\dfrac{y}{24}=\dfrac{z}{14}=\dfrac{x+y+z}{15+24+14}=-\dfrac{318}{53}=-6\)

=>x=-90; y=-144; z=-84