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\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{8}=\frac{y}{12}\)
\(\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{y}{12}=\frac{z}{15}\)
\(\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)
\(\Rightarrow\hept{\begin{cases}x=16\\y=24\\z=30\end{cases}}\)
a) Ta có \(\frac{x-1}{2}\)\(=\)\(\frac{y-2}{3}\)\(=\)\(\frac{z-3}{4}\)\(=\)\(\frac{2x-2}{4}\)\(=\)\(\frac{3y-6}{9}\)\(=\)\(\frac{\left(2x-2\right)+\left(3y-6\right)-\left(z-3\right)}{4+9-4}\)\(=\)\(\frac{\left(2x+3y-z\right)-5}{9}\)\(=\)\(\frac{50-5}{9}\)\(=\)5 Do đó x \(=\)5\(\times\)2\(+\)1\(=\)11 y\(=\)5\(\times\)3\(+\)2\(=\)17 z\(=\)5\(\times\)4\(+\)3\(=\)23
a) \(2x=3y=7z\)
\(\Rightarrow\frac{2x}{42}=\frac{3y}{42}=\frac{7z}{42}\)
\(\Rightarrow\frac{x}{21}=\frac{y}{14}=\frac{z}{6}\)
\(\Rightarrow\frac{3x}{63}=\frac{7y}{98}=\frac{5z}{30}\)
Áp dụng tính chất dãy tỉ số bằng nhau , ta có :
\(\frac{3x}{63}=\frac{7y}{98}=\frac{5z}{30}=\frac{3x-7y+5z}{63-98+30}=\frac{30}{-5}=-6\)
\(\Rightarrow\hept{\begin{cases}x=21.\left(-6\right)=-126\\y=14.\left(-6\right)=-84\\z=6.\left(-6\right)=-36\end{cases}}\)
b) \(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{2.4}=\frac{y}{3.4}\Rightarrow\frac{x}{8}=\frac{y}{12}\left(1\right)\)
\(\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{y}{4.3}=\frac{z}{5.3}\Rightarrow\frac{y}{12}=\frac{z}{15}\left(2\right)\)
Từ 1 và 2
\(\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)
Áp dụng tính chất dãy tỉ số bằng nhau ,ta có :
\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)
\(\Rightarrow\hept{\begin{cases}x=2.8=16\\y=2.12=24\\z=2.15=30\end{cases}}\)
\(\frac{2^{12}.3^5-4^6.81}{\left(2^2.3\right)^6+8^4.3^5}\)
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}\)
\(=\frac{2^{12}.\left(3^5-3^4\right)}{2^{12}.\left(3^6+3^5\right)}\)
\(=\frac{3^5-3^4}{3^6+3^5}=\frac{3^4.\left(3-1\right)}{3^5\left(3+1\right)}\)
\(=\frac{3^4.2}{3^5.4}=\frac{3^4.2}{3^4.3.4}=\frac{2}{12}=\frac{1}{6}\)
P/s: Hoq chắc ạ (: Ms lp 6 lm đại
\(\frac{x}{2}=\frac{y}{3}\)
\(\Leftrightarrow\frac{x}{8}=\frac{y}{12}\)(1)
\(\frac{y}{4}=\frac{z}{5}\)
\(\Leftrightarrow\frac{y}{12}=\frac{z}{15}\)(2)
Từ (1) (2)
\(\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)
\(\Rightarrow\hept{\begin{cases}x=2.8\\y=2.12\\z=2.15\end{cases}\Rightarrow}\hept{\begin{cases}x=16\\y=24\\z=30\end{cases}}\)
\(\frac{x+1}{3}=\frac{y+2}{4}=\frac{z+3}{5}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x+1}{3}=\frac{y+2}{4}=\frac{x+3}{5}=\frac{x+y+z+1+2+3}{3+4+5}=\frac{24}{12}=2\)
\(\Rightarrow\)\(\frac{x+1}{3}=2\Rightarrow x=5\)
\(\frac{y+2}{4}=2\Rightarrow y=6\)
\(\frac{z+3}{5}=2\Rightarrow z=7\)
Vậy bạn tự kết luận nha
Bài 1: Tìm x, y, z
\(\frac{x}{3}=\frac{y}{4}=>\frac{x}{3\times3}=\frac{y}{4\times3}=>\frac{x}{9}=\frac{y}{12}\)
\(\frac{y}{3}=\frac{z}{5}=>\frac{y}{3.4}=\frac{z}{5.4}=>\frac{y}{12}=\frac{z}{20}\)
=> \(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\)
- Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\) -> \(\frac{2x}{2\times9}=\frac{3y}{3\times12}=\frac{z}{20}\) -> \(\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}\)
-> \(\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)
\(\frac{x}{9}=3\rightarrow x=27\)
\(\frac{y}{12}=3\rightarrow y=36\)
\(\frac{z}{20}=3\rightarrow z=60\)
Vậy x = 27 ; y = 36 ; z = 60
Bài 2 : Tìm x, y:
5x = 2y và x.y = 40
Vì 5x = 2y => \(\frac{x}{2}=\frac{y}{5}\)
Cách 1:
\(\frac{x}{2}=\frac{y}{5}\) và x.y = 40
Đặt \(\frac{x}{2}=\frac{y}{5}\) = k
=> x = 2.k ; y = 5.k
x.y = 40 -> 2k = 5k = 40
-> 10 . \(k^2\) = 40
-> \(k^2\) = 4 -> k = 2 hoặc k = -2
k = 4 ta có : \(\frac{x}{2}=\frac{y}{5}=2->x=4;y=10\)
k = -4 ta có : \(\frac{x}{2}=\frac{y}{5}=-2->x=-4;y=-10\)
Cách 2:
\(\frac{x}{2}=\frac{y}{5}->\frac{x.x}{2}=\frac{x.y}{5}->\frac{x^2}{2}=\frac{40}{5}=\frac{x^2}{2}=8\)
=> \(x^2\) = 8 . 2 = 16 -> x = 4 hoặc -4
x = 4 -> 4.y = 40 => y = 10
x = -4 -> (-4).y = 40 => y = -10
Vậy x = 4 hoặc -4
y = 10 hoặc -10
\(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x}{9}=\frac{y}{12}\left(1\right)\\\frac{y}{3}=\frac{z}{5}\Rightarrow\frac{y}{12}=\frac{z}{15}\left(2\right)\)
Từ (1),(2) suy ra \(\frac{x}{9}=\frac{y}{12}=\frac{z}{15}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\frac{x}{9}=\frac{y}{12}=\frac{z}{15}=\frac{2x}{18}=\frac{-3y}{-36}=\frac{z}{15}=\frac{2x-3y+z}{18-\left(-36\right)+15}=\frac{6}{69}=\frac{2}{23}\)Suy ra x =\(\frac{2}{23}\cdot9=\frac{18}{23}\)
\(y=\frac{2}{23}\cdot12=\frac{24}{23}\\ z=\frac{2}{23}.15=\frac{30}{23}\)
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)}{2.2}=\frac{3\left(y-2\right)}{3.3}=\frac{z-3}{4}=\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}=k\)
Áp dụng TC DTSBN ta có :
\(k=\frac{\left(2x-2\right)+\left(3y-6\right)-\left(z-3\right)}{4+9-4}=\frac{\left(2x+3y-z\right)-5}{9}=\frac{50-5}{9}=5\)
\(\Rightarrow x-1=10;y-2=15;z-3=20\)
\(\Rightarrow x=11;y=17;z=23\)
ta có: \(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{8}=\frac{y}{12}\)
\(\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{y}{12}=\frac{z}{15}\)
\(\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)
ADTCDTSBN
có: \(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)
\(\Rightarrow\frac{x}{8}=2\Rightarrow x=16\)
y/12 = 2 => y = 24
z/15 = 2 => z = 30
KL: x = 16; y=24;z=30
Ta có :
\(\frac{x}{2}=\frac{y}{3}\)\(\Rightarrow\)\(\frac{x}{8}=\frac{y}{12}\)
\(\frac{y}{4}=\frac{z}{5}\)\(\Rightarrow\)\(\frac{y}{12}=\frac{z}{15}\)
Suy ra : \(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)
Do đó :
\(\frac{x}{8}=2\)\(\Rightarrow\)\(x=2.8=16\)
\(\frac{y}{12}=2\)\(\Rightarrow\)\(y=2.12=24\)
\(\frac{z}{15}=2\)\(\Rightarrow\)\(z=2.15=30\)
Vậy \(x=16\)\(;\)\(y=24\) và \(z=30\)
Chúc bạn học tốt ~