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\(\frac{15}{x-9}=\frac{20}{y-12}\Rightarrow\frac{x-9}{15}=\frac{y-12}{20}\Leftrightarrow\frac{x}{15}-\frac{3}{5}=\frac{y}{20}-\frac{3}{5}\)
\(\Rightarrow\frac{x}{15}=\frac{y}{20}\)
\(\Rightarrow\frac{x^2}{15^2}=\frac{x}{15}.\frac{y}{20}=\frac{1200}{300}=4=2^2\Rightarrow x^2=2^2.15^2=30^2\)
\(\Rightarrow x=30\text{ hoặc }x=-30\)
+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
\(\frac{y}{20}=\frac{x}{15}=-\frac{30}{15}=-2\Rightarrow y=-2.20=-40\)
\(\frac{40}{z-24}=\frac{15}{-30-9}=-\frac{15}{3}\Rightarrow z=\frac{-3.40}{15}+24=16\)
\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\Rightarrow\frac{x-9}{y-12}\)
\(\Rightarrow\frac{3}{4}=\frac{x-9}{y-12}=\frac{9}{12}=\frac{x-9}{y-12}=\frac{x-9+9}{y-12+12}\)\(=\frac{x}{y}=\frac{xy}{y^2}=\frac{x^2}{xy}\)
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)
\(\Rightarrow\left[\begin{array}{nghiempt}x-9=15k\\y-12=20k\\z-24=40k\end{cases}\Rightarrow\left[\begin{array}{nghiempt}x=15k+9\\y=20k+12\\z=40k+24\end{array}\right.}\)
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
MÌNH KO BIẾT ĐÚNG KO ĐÂU NHA
pt :15/(x-9)=20/(y-12) <=> 60/(4x-36)=60/(3y-36) : (Quy đồng mẫu)
=> 4x=3y
<=> x= 3y/4
kết hợp với xy= 1200 => x=30 hoặc x=-30 =>y =+-40
thế x hoặc y vào pt ban đàu ta có z= 80 (pt là phân tích, mìh ko bít gõ phân số nên thông cảm :D)
Ta có : 15/(x-9)= 20/(y-12)
<=> 15(y-12) = 20(x-9)
<=> 15y - 180 = 20x - 180
<=> 3y = 4x
<=> y = 4/3x
Do xy = 1200
=> 4/3. x^2 = 1200
=> x^2 = 1200 : 4/3
=> x^2 = 900
<=> x = 30
<=> y = 40
<=> 5/7 = 40/(z-24)
<=> 80 = z
=> x=30 ; y=40 ; z=80
\(\frac{15}{x-9}=\frac{20}{y-12}\Leftrightarrow15\left(y-12\right)=20\left(x-9\right)\Leftrightarrow15y-180=20x-180\Leftrightarrow15y=20x\Leftrightarrow\frac{y}{20}=\frac{x}{15}\Leftrightarrow\frac{xy}{20}=\frac{x^2}{15}\Leftrightarrow x^2=\frac{15.1200}{20}=900\Leftrightarrow\orbr{\begin{cases}x=30\\x=-30\end{cases}}\)
Chia từng trường hợp tìm y, z.
mk hoc lop 6 soryy ko giup duoc