Cho \(\frac{40}{x-30}\)= \(\frac{20}{y-15}\)= \(\frac{28}{z-21}\) và x.y.z = 22400
Tìm x, y, z
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DH
1
BT
8 tháng 11 2017
\(\frac{40}{x-30}=\frac{20}{y-15}=>2y-30=x-30=>x=2y.\)
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
XO
1 tháng 11 2019
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
VH
1 tháng 11 2019
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
31 tháng 7 2016
\(\Rightarrow\left[\begin{array}{nghiempt}x-9=15k\\y-12=20k\\z-24=40k\end{cases}\Rightarrow\left[\begin{array}{nghiempt}x=15k+9\\y=20k+12\\z=40k+24\end{array}\right.}\)
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
MR
3
1 tháng 1 2020
áp dụng DSTCBN:
Ta có:
\(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}\Leftrightarrow\frac{x-30}{40}=\frac{y-15}{20}=\frac{z-21}{28}\)
\(\Rightarrow\frac{x-30}{10}=\frac{y-15}{5}=\frac{z-21}{7}\)
\(\frac{\Rightarrow x}{10}-\frac{30}{10}=\frac{y}{5}-\frac{15}{5}=\frac{z}{7}-\frac{21}{7}\)
\(\frac{\Rightarrow x}{10}-3=\frac{y}{3}-3=\frac{z}{7}-3\)
\(\frac{\Rightarrow x}{10}=\frac{y}{5}=\frac{z}{7}\)
\(\frac{x}{10}=\frac{y}{5}=\frac{z}{7}=t=\hept{\begin{cases}x=10t\\y=5t\\z=7t\end{cases}}\)
\(xyz=22400\Leftrightarrow350t^3=22400\Leftrightarrow t^3=64\Rightarrow t=4\)
\(\Rightarrow\hept{\begin{cases}x=40\\y=20\\z=28\end{cases}}\)
HT
1 tháng 1 2020
\(\text{Ta có:}\)\(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}\)
\(\Leftrightarrow\frac{x-30}{40}=\frac{y-15}{40}=\frac{z-21}{28}\)
\(\Leftrightarrow\frac{x}{40}-\frac{30}{40}=\frac{y}{40}-\frac{15}{40}=\frac{z}{28}-\frac{21}{28}\)
\(\Leftrightarrow\frac{x}{40}-\frac{3}{4}=\frac{y}{20}-\frac{3}{4}=\frac{z}{28}-\frac{3}{4}\)\
\(\Leftrightarrow\frac{x}{40}=\frac{y}{20}=\frac{z}{28}\)
\(\text{đặt:}\)\(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=k\)
\(\Rightarrow x=40k\)
\(\Rightarrow y=20k\)
\(\Rightarrow z=28k\)
\(\text{Theo đề ta có :}\)\(x.y.z=22400\Rightarrow40k.20k.28k=22400\)
\(\Rightarrow22400.k^3=22400\)
\(\Rightarrow k^3=1\)
\(\Rightarrow k=\pm1\)
\(\text{Với k=1 thì :}\)\(\hept{\begin{cases}x=40\\y=20\\z=28\end{cases}}\)
\(\text{Với k=-1 thì :}\)\(\hept{\begin{cases}x=-40\\y=-20\\z=-28\end{cases}}\)
NT
0
Ta có: \(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}.\)
\(\Rightarrow\frac{x-30}{40}=\frac{y-15}{20}=\frac{z-21}{28}.\)
\(\Rightarrow\frac{x}{40}-\frac{3}{4}=\frac{y}{20}-\frac{3}{4}=\frac{z}{28}-\frac{3}{4}\)
\(\Rightarrow\frac{x}{40}=\frac{y}{20}=\frac{z}{28}\) và \(x.y.z=22400.\)
Đặt \(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=k\Rightarrow\left\{{}\begin{matrix}x=40k\\y=20k\\z=28k\end{matrix}\right.\)
Có: \(x.y.z=22400\)
=> \(40k.20k.28k=22400\)
=> \(22400.k^3=22400\)
=> \(k^3=22400:22400\)
=> \(k^3=1\)
=> \(k=1.\)
Với \(k=1.\)
\(\Rightarrow\left\{{}\begin{matrix}x=40.1=40\\y=20.1=20\\z=28.1=28\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)=\left(40;20;28\right).\)
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