\(\dfrac{15}{x-9}=\dfrac{20}{y-12}=\dfrac{40}{z-24}\)

\(\Rightarrow\dfrac{x-9}{15}=\dfrac{y-12}{20}=\dfrac{z-24}{40}=k\)

\(\Rightarrow\left(15k+9\right)\left(20k+12\right)=1200\)

\(\Rightarrow3.4\left(5k+3\right)\left(5k+3\right)=1200\)

\(\Rightarrow\left(5k+3\right)\left(5k+3\right)=1200:3:4\)

\(\Rightarrow\left(5k+3\right)^2=100\)

\(\Rightarrow\left[{}\begin{matrix}5k+3=10\\5k+3=-10\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}k=\dfrac{7}{5}\\k=\dfrac{-13}{5}\end{matrix}\right.\)

+) Với \(k=\dfrac{7}{5}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7}{5}.15+9\\y=\dfrac{7}{5}.20+12\\z=\dfrac{7}{5}.40+24\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=30\\y=40\\z=80\end{matrix}\right.\)

+) Với \(k=\dfrac{-13}{5}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-13}{5}.15+9\\y=\dfrac{-13}{5}.20+12\\z=\dfrac{-13}{5}.40+24\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-30\\y=-40\\z=-80\end{matrix}\right.\)

Vậy ................................

Chúc bạn học tốt!

\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\Rightarrow\frac{x-9}{y-12}\)

\(\Rightarrow\frac{3}{4}=\frac{x-9}{y-12}=\frac{9}{12}=\frac{x-9}{y-12}=\frac{x-9+9}{y-12+12}\)\(=\frac{x}{y}=\frac{xy}{y^2}=\frac{x^2}{xy}\)

Từ \(\frac{3}{4}=\frac{xy}{y^2}\Rightarrow\frac{3}{4}=\frac{1200}{y^2}\Rightarrow y^2=1200\cdot\frac{4}{3}=20^2\Rightarrow y=\pm40\)

• Nếu y=40 => x= 1200: 40 = 30 

Mà \(\frac{15}{x-9}=\frac{40}{z-24}\Rightarrow z=80\)

• Nếu y = -40 => x = 1200:(-40) = - 30 

Mà \(\frac{15}{x-9}=\frac{40}{z-24}\Rightarrow z=-80\)

Vây (x , y , z ) = ( 30, 40, 80); ( - 30; -40; -80) 

\(\frac{15}{x-9}=\frac{20}{y-12}\Rightarrow\frac{x-9}{15}=\frac{y-12}{20}\Leftrightarrow\frac{x}{15}-\frac{3}{5}=\frac{y}{20}-\frac{3}{5}\)

\(\Rightarrow\frac{x}{15}=\frac{y}{20}\)

\(\Rightarrow\frac{x^2}{15^2}=\frac{x}{15}.\frac{y}{20}=\frac{1200}{300}=4=2^2\Rightarrow x^2=2^2.15^2=30^2\)

\(\Rightarrow x=30\text{ hoặc }x=-30\)

+TH1: x = 30

\(\frac{y}{20}=\frac{x}{15}\Rightarrow y=\frac{20.x}{15}=\frac{20.30}{15}=40\)

\(\frac{40}{z-24}=\frac{15}{30-9}=\frac{5}{7}\Rightarrow z=\frac{40.7}{5}+24=80\)

+TH2: x = -30

\(\frac{y}{20}=\frac{x}{15}=-\frac{30}{15}=-2\Rightarrow y=-2.20=-40\)

\(\frac{40}{z-24}=\frac{15}{-30-9}=-\frac{15}{3}\Rightarrow z=\frac{-3.40}{15}+24=16\)

\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{24}{z-24}\Rightarrow\)\(\frac{x-9}{15}=\frac{y-12}{20}=\frac{z-24}{40}=k\)

Do x . y = 1200 => ( 15k + 9) ( 20k + 12) = 1200

3(5k+3).4(5k+3) = 1200

12 ( 5k+3)² = 1200

( 5k+3)² =  100 hoặc ( 5k+3)² =  -100

=> 5k+3 = 10 hoặc 5k+3 = -10

=> 5k = 7 hoặc 5k = -13

=> k = 7/5 hoặc k = -13/5

 Vậy

\(\hept{\begin{cases}\text{x = 15 . \frac{7}{5}+9 = 30}\\y=20.\frac{7}{5}+12=40\\z=40.\frac{7}{5}+24=80\end{cases}}\)\(\hept{\begin{cases}x=15.\frac{7}{5}+9=30\\y=20.\frac{7}{5}+12=40\\z=40.\frac{7}{5}+24=80\end{cases}}\)hoặc\(\hept{\begin{cases}x=15.\frac{-13}{5}+9=-30\\y=20.\frac{-13}{5}+12=-40\\z=40.\frac{-13}{5}+24=-80\end{cases}}\)

mk hoc lop 6 soryy ko giup duoc