\(a.\) Tìm các số x,y,z biết rằng: 3x = 4y, 5y = 6z và xyz = 30
b. Tìm x biết: \(\left|x-\dfrac{1}{2}\right|+\dfrac{3}{4}=\left|-1.6+\dfrac{3}{5}\right|\)
Tìm x,y,z biết :
1) \(x:y:z=3:5:\left(-2\right)\) và \(5x-y+3z=-16\)
2) \(\dfrac{x}{2}=\dfrac{y}{-3};\dfrac{z}{3}=\dfrac{y}{4}\) và \(x+y+z=5,2\)
3) \(2x=3y;7z=5y\) và \(3x-7y+5z=30\)
4) \(3x=4y=5z\) và \(x-\left(y+z\right)=-21\)
5) \(\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}\) và \(2x+3y-z=50\)
tìm các số x , y , z biết rằng : 3x = 4y , 5y = 6z va xyz = 30
tìm x : \(\left|x-\frac{1}{2}\right|+\frac{3}{4}=\left|-1,6+\frac{3}{5}\right|\)
\(\left|x-\frac{1}{2}\right|+\frac{3}{4}=\left|-1,6+\frac{3}{5}\right|\)
\(\Rightarrow\left|x-\frac{1}{2}\right|+\frac{3}{4}=\left|-1,6+0,6\right|\)
\(\Rightarrow\left|x-\frac{1}{2}\right|+\frac{3}{4}=\left|-1\right|\)
\(\Rightarrow\left|x-\frac{1}{2}\right|+\frac{3}{4}=1\)
\(\Rightarrow\left|x-\frac{1}{2}\right|=1-\frac{3}{4}\)
\(\Rightarrow\left|x-\frac{1}{2}\right|=\frac{1}{4}\)
\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{2}=\frac{1}{4}\\x-\frac{1}{2}=-\frac{1}{4}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=\frac{1}{4}\end{cases}}}\)
Vậy ...
\(1)\) Ta có :
\(3x=4y\)\(\Leftrightarrow\)\(\frac{x}{4}=\frac{y}{3}\)\(\Leftrightarrow\)\(\frac{x}{8}=\frac{y}{6}\)
\(5y=6z\)\(\Leftrightarrow\)\(\frac{y}{6}=\frac{z}{5}\)
\(\Rightarrow\)\(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}\)
Đặt \(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}=k\)\(\Rightarrow\)\(\hept{\begin{cases}x=8k\\y=6k\\z=5k\end{cases}}\) \(\left(1\right)\)
Thay \(\left(1\right)\) vào \(xyz=30\) ta được :
\(8k.6k.5k=30\)
\(\Leftrightarrow\)\(240k^3=30\)
\(\Leftrightarrow\)\(k^3=\frac{30}{240}\)
\(\Leftrightarrow\)\(k^3=\frac{1}{8}\)
\(\Leftrightarrow\)\(k^3=\left(\frac{1}{2}\right)^3\)
\(\Leftrightarrow\)\(k=\frac{1}{2}\)
Suy ra :
\(x=8k=8.\frac{1}{2}=\frac{8}{2}=4\)
\(y=6k=6.\frac{1}{2}=\frac{6}{2}=3\)
\(z=5k=5.\frac{1}{2}=\frac{5}{2}\)
Vậy \(x=4\)\(;\)\(y=3\) và \(z=\frac{5}{2}\)
Chúc bạn học tốt ~
Ta có :
\(3x=4y\Rightarrow\frac{x}{4}=\frac{y}{3}\Rightarrow\frac{x}{8}=\frac{y}{6}\left(1\right)\)
\(5y=6z\Rightarrow\frac{y}{6}=\frac{z}{5}\left(2\right)\)
Từ \(\left(1\right);\left(2\right)\)
\(\Rightarrow\frac{x}{8}=\frac{y}{6}=\frac{z}{5}\)
Đặt \(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}=k\left(k\ne0\right)\)
\(\Rightarrow x=8k;y=6k;z=5k\)
\(\Rightarrow xyz=8k.6k.5k\)
\(\Rightarrow xyz=240k^3\)
Do \(xyz=30\)
\(\Rightarrow240k^3=30\)
\(\Rightarrow k^3=\frac{1}{8}\)
\(\Rightarrow k=\frac{1}{2}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{1}{2}.8=4\\y=\frac{1}{2}.6=3\\z=\frac{1}{2}.5=2,5\end{cases}}\)
Vậy \(x=4;y=3;z=2,5\)
Giúp mk nha
a) Tìm các số x, y, z biết rằng
3x=4y ; 5y=6z và xyz = 30
b) \(|x-\dfrac{1}{2}|+\dfrac{3}{4}=|-1,6+\dfrac{3}{5}|\)
Ta có : \(3x=4y\Rightarrow\dfrac{x}{4}=\dfrac{y}{3}\Rightarrow\dfrac{x}{24}=\dfrac{y}{18}\left(1\right)\)
\(5y=6z\Rightarrow\dfrac{y}{6}=\dfrac{z}{5}\Rightarrow\dfrac{y}{18}=\dfrac{z}{15}\left(2\right)\)
Từ (1);(2) \(\Rightarrow\dfrac{x}{24}=\dfrac{y}{18}=\dfrac{z}{15}\)
Đặt \(\dfrac{x}{24}=\dfrac{y}{18}=\dfrac{z}{15}=k\Rightarrow x=24k;y=18k;z=15k\)
\(\text{Ta có }:x.y.z=24k.18k.15k=30\\ \Rightarrow k^3.6480=30\\ \Rightarrow k^3=\dfrac{1}{216}\\ \Rightarrow k=\dfrac{1}{6}\\ \Rightarrow x=24.\dfrac{1}{6}=4\\ y=18.\dfrac{1}{6}=3\\ z=15.\dfrac{1}{6}=2.5\)
Vậy x = 4 ; y = 3 ; z = 2,5
a) Tìm các số x, y, z biết rằng
3x=4y ; 5y=6z và xyz = 30
Giải
Ta có: 3x = 4y; 5y = 6z \(\Rightarrow\dfrac{x}{4}=\dfrac{y}{3}\); \(\dfrac{y}{6}=\dfrac{z}{5}\)
\(\Rightarrow\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{5}\)
Đặt \(\dfrac{x}{8}=\dfrac{y}{6}=\dfrac{z}{5}=k\) \(\Rightarrow\left\{{}\begin{matrix}x=8k\\y=6k\\z=5k\end{matrix}\right.\)
Có \(xyz=30\) \(\Leftrightarrow\) \(8k.6k.5k=30\)
\(\Rightarrow\) \(240k^3=30\)
\(\Rightarrow\) \(k^3=8\)
\(\Rightarrow\) \(k=\sqrt[3]{8}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=8.2=16\\y=6.2=12\\z=5.2=10\end{matrix}\right.\)
a) Tìm tập hợp các số nguyên x, biết rằng\(4\dfrac{5}{9}:2\dfrac{5}{18}-7< x< \left(3\dfrac{1}{5}:3,2+4,5.1\dfrac{31}{45}\right):\left(-21\dfrac{1}{2}\right)\)
b) tìm x, biết \(\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{6}\right|+\left|x+\dfrac{1}{12}\right|+\left|x+\dfrac{1}{20}\right|+....+\left|x+\dfrac{1}{110}\right|-11x\)
c)Tính gt biểu thức \(C=2x^3-5y^3+2015\) tại x,y thỏa mãn \(\left|x-1\right|+\left(y+2\right)^{20}=0\)
a,Tìm x,y,z biết/: \(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\) và \(x^2-y^2=-16\)
b, Tìm x biết: \(\left|2x+3\right|=x+2\)
a) \(\dfrac{x}{2}=\dfrac{y}{3}\Rightarrow\dfrac{x^2}{4}=\dfrac{y^2}{9}=\dfrac{x^2-y^2}{4-9}=\dfrac{-16}{-5}=\dfrac{16}{5}\)
\(\Rightarrow\left\{{}\begin{matrix}x^2=4.\dfrac{16}{5}\\y^2=9.\dfrac{16}{5}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\pm\left(2.\dfrac{4}{\sqrt[]{5}}\right)=\pm\dfrac{8\sqrt[]{5}}{5}\\y=\pm\left(3.\dfrac{4}{\sqrt[]{5}}\right)=\pm\dfrac{12\sqrt[]{5}}{5}\end{matrix}\right.\)
\(\dfrac{y}{4}=\dfrac{z}{5}\Rightarrow z=\dfrac{5}{4}y=\dfrac{5}{4}.\left(\pm\dfrac{12\sqrt[]{5}}{5}\right)=\pm3\sqrt[]{5}\)
b) \(\left|2x+3\right|=x+2\)
\(\Rightarrow\left[{}\begin{matrix}2x+3=x+2\\2x+3=-x-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\3x=-5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\3x=-\dfrac{5}{3}\end{matrix}\right.\)
Đính chính
Dòng cuối \(3x=-\dfrac{5}{3}\rightarrow x=-\dfrac{5}{3}\)
Tìm các số x, y, z biết rằng \(3x=4y\), \(5y=6z\) và \(xyz=30\)
3x=4y
=>x/4=y/3
=>x/8=y/6
5y=6z
=>y/6=z/5
=>x/8=y/6=z/5
Đặt x/8=y/6=z/5=k
=>x=8k; y=6k; z=5k
xyz=30
=>8k*6k*5k=30
=>240k^3=30
=>k^3=1/8
=>k=1/2
=>x=8*1/2=4; y=6*1/2=3; z=5*1/2=5/2
cho x,y,z là các số thực dương thỏa mãn x+y+z=xyz.CMR
\(\dfrac{x}{1+x^2}+\dfrac{2y}{1+y^2}+\dfrac{3z}{1+z^2}=\dfrac{xyz\left(5x+4y+3z\right)}{\left(x+y\right)\left(y+z\right)\left(z+x\right)}\)
Tìm x biết:
\(a,\left(x-\dfrac{3}{4}\right)+50\%=\dfrac{1}{6}\)
\(b,\dfrac{1}{2}x-\dfrac{5}{6}x=\dfrac{7}{2}\)
\(c,\left(4-x\right)\left(3x+5\right)=0\)
\(d,\dfrac{x}{16}=\dfrac{50}{32}\)
\(e,\left(2x-3\right)+\dfrac{3}{2}=-\dfrac{1}{4}\)
a: =>x-3/4=1/6-1/2=1/6-3/6=-2/6=-1/3
=>x=-1/3+3/4=-4/12+9/12=5/12
b: =>x(1/2-5/6)=7/2
=>-1/3x=7/2
hay x=-21/2
c: (4-x)(3x+5)=0
=>4-x=0 hoặc 3x+5=0
=>x=4 hoặc x=-5/3
d: x/16=50/32
=>x/16=25/16
hay x=25
e: =>2x-3=-1/4-3/2=-1/4-6/4=-7/4
=>2x=-7/4+3=5/4
hay x=5/8
tìm x biết:
a) \(5^x.\left(5^3\right)^2=625\)
b)\(\left(\dfrac{12}{15}\right)^x=\left(\dfrac{5}{3}\right)^{-5}-\left(-\dfrac{3}{5}\right)^4\)
c)\(\left(-\dfrac{3}{4}\right)^{3x-1}=\dfrac{256}{81}\)
d)\(172x^2-7^9:98^3=2^{-3}\)