\(\Rightarrow\left[\begin{array}{nghiempt}x-9=15k\\y-12=20k\\z-24=40k\end{cases}\Rightarrow\left[\begin{array}{nghiempt}x=15k+9\\y=20k+12\\z=40k+24\end{array}\right.}\)

ta có:

x.y=1200\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\Rightarrow\frac{x-9}{15}=\frac{y-12}{20}=\frac{z-24}{40}=k\)

=> (15k+9)(20k+12)=1200

=> 3.4(5k+3)(5k+3)=1200

=> (5k+3)²=100

=> 5k+3=\(\pm\)10

 => \(\left[\begin{array}{nghiempt}5k+3=10\\5k+3=-10\end{cases}\Rightarrow\left[\begin{array}{nghiempt}5k=7\\5k=-13\end{cases}\Rightarrow}\left[\begin{array}{nghiempt}k=\frac{7}{5}\\k=-\frac{13}{5}\end{array}\right.}\)

* với k=7/5

x=7/5x15+9=30

y=7/5x20+12=40

z=7/5x40+24=80

* với k=-13/5

x=-13/5x15+9=-30

y=-13/5x20+12=-40

z=-13/5x40+24=-80

b)

\(\frac{40}{x-30}=\frac{20}{y-50}=\frac{28}{z-21}\Rightarrow\frac{x-30}{40}=\frac{y-50}{20}=\frac{z-21}{28}k=\)

=>\(\left[\begin{array}{nghiempt}x-30=40k\\y-50=20k\\z-21=28k\end{cases}\Rightarrow\left[\begin{array}{nghiempt}x=40k+30\\y=20k+50\\z=28k+21\end{array}\right.}\)

ta có:

x.y.z=22400

=> (40k+30)(20k+50)(28k+21)=22400

c) 15x=-10y=6z

\(\Rightarrow\frac{15x}{30}=\frac{-10y}{30}=\frac{6z}{30}\Rightarrow\frac{x}{2}=-\frac{y}{3}=\frac{z}{5}=k\)

=> \(\left[\begin{array}{nghiempt}x=2k\\y=-3k\\z=5k\end{array}\right.\)

ta có:

x.y.z=30000

=> 2k.(-3k).5k=30000

=> k³=1000

=> k=10

ta có: x=10x2=20

          y=10.(-3)=-30

          z=10.5=50

giúp mk vs ! mai đi hok ùi

mk ms lm đc câu a và c

dạng nhân này thì bạn đặt =k sẽ ra cả nha,mk ngại đánh lắm

\(\frac{40}{x-30}=\frac{20}{y-15}=>2y-30=x-30=>x=2y.\)

Tương tự: \(\frac{40}{x-30}=\frac{28}{z-21}< =>\frac{10}{x-30}=\frac{7}{z-21}=>10z-210=7x-210=>7x=10z\)

\(\frac{20}{y-15}=\frac{28}{z-21}< =>\frac{5}{y-15}=\frac{7}{z-21}=>5z-105=7y-105=>7y=5z\)

Ta có: x.y.z=22400 <=> 2y.y.7y/5=22400

=> y³=22400.5/14=8000=20³  => y=20  => z=7.20:5=28 ; x=2.20=40

Đáp số: x=40; y=20; z=28

40/x-30=20/y-15=28/z-21 => 40/x-40/30=20/y-20/15=28/z-28/21 => 40/x-4/3=20/y-4/3=28/z-4/3

<=> 40/x=20/y=28/z=K => x=40.K; y=20.K; z=28.K

<=> xyz=40.20.28.K³ => xyz=22400.K³ 

<=>K³=1 => K=+-1

<=> x=40.K = 40.1=40 (1)

                   =40.(-1)=-40

TH(1): x=40 => y=20; z =28

TH(2); x=-40 => y=-20; z=-28

vậy x=40; y=20; z =28

hoặc x=-40; y=-20; z=-28

câu b làm y vậy đó bạn đổi 15x=-10y=6z=>x/1/15=y/-1/10=z/1/6

1/2x X 1/3 x X + 1/6 x X = 28/21

Từ đẳng thức : \(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}\)

\(\Rightarrow1:\frac{40}{x-30}=1:\frac{20}{y-15}=1:\frac{28}{z-21}\)

\(\Rightarrow\frac{x-30}{40}=\frac{y-15}{20}=\frac{z-21}{28}\)

\(\Rightarrow\frac{x}{40}-\frac{3}{4}=\frac{y}{20}-\frac{3}{4}=\frac{z}{28}-\frac{3}{4}\)

\(\Rightarrow\frac{x}{40}=\frac{y}{20}=\frac{z}{28}\)

Đặt \(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=k\Rightarrow\hept{\begin{cases}x=40k\\y=20k\\z=28k\end{cases}}\)

Khi đó : xyz = 22400

<=> 40k.20k.28k = 22400

=> 22400.k³ = 22400

=> k³ = 1

=> k³ = 1³

=> k = 1

Khi đó : x = 40.1 = 40 ; 

              y = 20.1 = 20;

              z = 28.1 = 28 

Vậy x = 40 ; y = 20 ; z = 28

Ta có:\(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}\)

hay\(\frac{x-30}{40}=\frac{y-15}{20}=\frac{z-21}{28}\)

\(=\frac{x}{40}-\frac{3}{4}=\frac{y}{20}-\frac{3}{4}=\frac{z}{28}-\frac{3}{4}\)

\(\Rightarrow\)\(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}\)

\(\Rightarrow\)\(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=\frac{x.y.z}{40.20.28}=\frac{22400}{22400}=1\)

\(\Rightarrow\)\(\hept{\begin{cases}\frac{x}{40}=1\\\frac{y}{20}=1\\\frac{z}{28}=1\end{cases}}\)\(\Rightarrow\)\(\hept{\begin{cases}x=40\\y=20\\z=28\end{cases}}\)

Vậy x=40; y=20; z=28

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