tìm giá trị của 2x+y-z biết x/5=y/-4=z/6 và xyz=15. AI giúp mk, mk tick cho
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a) \(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7};x+y+z=56\)
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x+y+z}{2+5+7}=\dfrac{56}{14}=4\)
\(\Rightarrow\left\{{}\begin{matrix}x=4.2=8\\y=4.5=20\\z=4.7=28\end{matrix}\right.\)
b) \(\dfrac{x}{1,1}=\dfrac{y}{1,3}=\dfrac{z}{1,4}\left(1\right);2x-y=5,5\)
\(\left(1\right)\Rightarrow\dfrac{2x-y}{1,1.2-1,3}=\dfrac{5,5}{0,9}\)
\(\Rightarrow\left\{{}\begin{matrix}x=1,1.\dfrac{5,5}{0,9}=\dfrac{6,05}{0,9}\\y=1,3.\dfrac{5,5}{0,9}=\dfrac{7,15}{0,9}\\z=\dfrac{1,4}{1,1}.x=\dfrac{1,4}{1,1}.\dfrac{6,05}{0,9}=\dfrac{8,47}{0,99}\end{matrix}\right.\)
d) \(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5};xyz=-30\)
\(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5}=\dfrac{xyz}{2.3.5}=\dfrac{-30}{30}=-1\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.\left(-1\right)=-2\\y=3.\left(-1\right)=-3\\z=5.\left(-1\right)=-5\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
Ta có:
\(y-x=25\Rightarrow y=25+x\)
Mà \(7x=4y\Rightarrow7x=4\cdot\left(25+x\right)\)
\(7x=100+4x\)
\(\Rightarrow7x-4x=100\)
\(3x=100\)
\(x=\frac{100}{3}\)
bài 1 :
Ta có: 7x=4y ⇔ x/4=y/7
áp dụng tính chất dãy tỉ số bằng nhau ta có
x/4=y/7=(y-x)/(7-4)=100/3
⇒x= 4 x 100/3=400/3 ; y = 7 x 100/3=700/3
bài 2
ta có x/5 = y/6 ⇔ x/20=y/24
y/8 = z/7 ⇔ y/24=z/21
⇒x/20=y/24=z/21
ADTCDTSBN(bài 1 có)
x/20=y/24=z/21=(x+y)/(20+24)=69/48=23/16
⇒x= 20 x 23/16 = 115/4
y= 24x 23/16=138/2
z=21x23/16=483/16
![](https://rs.olm.vn/images/avt/0.png?1311)
gợi ý nhé
xyz=4900 (=) 70xyz=343000 (=) 2x*7y*5z=343000
áp dụng giả thiết đề bài =) 8x3=343000 =) x=35
=) 7y =70 (=) y=10
=) 5z = 70 (=) z= 14
vậy ...
chúc bn hc tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
a )
Ta có :
\(\hept{\begin{cases}\frac{x}{5}=\frac{y}{6}\\\frac{y}{8}=\frac{z}{7}\end{cases}\Rightarrow\hept{\begin{cases}\frac{x}{20}=\frac{y}{24}\\\frac{y}{24}=\frac{z}{21}\end{cases}}}\)
và \(x+y-z=69\)
ADTCDTSBN , ta có :
\(\frac{x}{20}=\frac{y}{24}=\frac{z}{21}=\frac{x+y-z}{20+24-21}=\frac{69}{23}=3\)
\(\Rightarrow\hept{\begin{cases}\frac{x}{20}=3\\\frac{y}{24}=3\\\frac{z}{21}=3\end{cases}\Rightarrow\hept{\begin{cases}x=3.20=60\\y=3.24=72\\z=3.21=63\end{cases}}}\)
Vậy ...
b )
Ta có :
\(5y=72\Rightarrow y=\frac{72}{5}=14,4\)
\(\Rightarrow x=14,4.3:2=21,6\)
và \(3x+5y-7z=30\)
Thay vào làm tiếp :
c )
\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)
\(=\frac{3\left(x-1\right)}{6}=\frac{4\left(y+3\right)}{16}=\frac{5\left(z-5\right)}{30}\)
\(=\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)
\(=\frac{5z-25-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}\)( ADTCDTSBN )
\(=\frac{5z-25-3x+3-4y-12}{8}=\frac{5z-3x-4y-34}{8}\)
\(=\frac{50-34}{8}=\frac{16}{8}=2\)
\(\Rightarrow\hept{\begin{cases}\frac{x-1}{2}=2\\\frac{y+3}{4}=2\\\frac{z-5}{6}=2\end{cases}\Rightarrow\hept{\begin{cases}x-1=2.2=4\\y+3=2.4=8\\z-5=2.6=12\end{cases}\Rightarrow}\hept{\begin{cases}x=5\\y=5\\z=17\end{cases}}}\)
Vậy ...
Áp dụng tính chất dãy tỉ số bằng nhau
\(\frac{x}{5}=\frac{y}{7}=\frac{z}{9}=\frac{x-y+z}{5-7+9}=\frac{315}{7}=45\)
suy ra: x/5 = 45 => x = 225
y/7 = 45 => y = 315
z/9 = 45 => z = 405
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(\frac{x}{5}=\frac{y}{-4}=\frac{z}{6}=k\)
=> x=5k ; y=-4k ; z=6k
=> xyz=5k.(-4k).6k=-120k^3
15=-120k^3
k^3=-1/8
k=-1/2
Từ \(\frac{x}{5}=-\frac{1}{2}\Rightarrow x=-\frac{5}{2}\)
\(\frac{y}{-4}=-\frac{1}{2}\Rightarrow y=2\)
\(\frac{z}{6}=-\frac{1}{2}\Rightarrow z=-3\)
Vậy 2x+y-z=-5/2 x 2 + 2 -(-3)=0
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x}{5}=\frac{y}{7}\Rightarrow\frac{x}{15}=\frac{x}{21};\frac{y}{3}=\frac{z}{4}\Rightarrow\frac{y}{21}=\frac{z}{28}\Rightarrow\frac{x}{15}=\frac{y}{21}=\frac{z}{28}=\frac{x+y+z}{15+21+28}=\frac{192}{64}=3\)
\(\Rightarrow\hept{\begin{cases}x=15.3=45\\y=21.3=63\\z=28.3=84\end{cases}}\)
Vậy: x=45; y=63;z=84
Theo bài ra ta có :
\(\frac{x}{5}\)=\(\frac{y}{7}\)\(\Rightarrow\frac{x}{15}\)=\(\frac{y}{21}\)
\(\frac{y}{3}=\frac{z}{4}\Rightarrow\frac{y}{21}=\frac{z}{28}\)
\(\Rightarrow\)\(\frac{x}{15}=\frac{y}{21}=\frac{z}{28}\)và x+y+z=192
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{15}=\frac{y}{21}=\frac{z}{28}=\frac{x+y+z}{15+21+28}=\frac{192}{64}=3\)
\(\Rightarrow\hept{\begin{cases}x=3.15=45\\y=3.21=63\\z=3.28=74\end{cases}}\)
Nhớ k mk nha
![](https://rs.olm.vn/images/avt/0.png?1311)
a) ADTCDTSBN
có: \(\frac{x}{12}=\frac{y}{13}=\frac{z}{15}=\frac{x+y+z}{12+13+15}=\frac{160}{40}=4\)
=> x/12 = 4 => x = 48
...
b) ta có: \(x=\frac{y}{6}=\frac{z}{3}=\frac{2x}{2}=\frac{3y}{18}=\frac{4z}{12}\)
ADTCDTSBN
có: \(\frac{2x}{2}=\frac{3y}{18}=\frac{4z}{12}=\frac{2x-3y+4z}{2-18+12}=\frac{16}{-4}=-4\)
=>...
c) ta có: \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{3}=\frac{2x}{4}=\frac{3y}{-9}=\frac{2z}{8}\)
ADTCTDBN
có: \(\frac{2x}{4}=\frac{3y}{-9}=\frac{2z}{8}=\frac{2x+3y+2z}{4-9+8}=\frac{1}{3}\)
=>...