Tìm x,y,z biết:
a. \(x=\dfrac{y}{6}=\dfrac{z}{3}và2x-3x-4z=24\)
\(b.6x=10y=15z\) và \(x+y-z=90\)
\(c.\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}và5z-3x-4y=50\)
\(d.\dfrac{x}{4}=\dfrac{y}{3};\dfrac{y}{5}=\dfrac{z}{3}vàx-y+100=z\)
1.\(x=\dfrac{y}{6}=\dfrac{z}{3}và2x-3y+4z=24\)
2.\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}và5z-3x-4y=50\)
3.\(6x=10y=15zvàx+y-z=90\)
\(1,\dfrac{x}{1}=\dfrac{y}{6}=\dfrac{z}{3}=\dfrac{2x-3y+4z}{2-18+12}=\dfrac{24}{-4}=-6\\ \Leftrightarrow\left\{{}\begin{matrix}x=-6\\y=-36\\z=-18\end{matrix}\right.\\ 2,\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}=\dfrac{-3x+3-4y-12+5z-25}{-6-16+30}=\dfrac{50-34}{8}=\dfrac{16}{8}=2\\ \Leftrightarrow\left\{{}\begin{matrix}x-1=4\\y+3=8\\z-5=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=5\\z=17\end{matrix}\right.\)
\(3,6x=10y=15z\Leftrightarrow\dfrac{6x}{30}=\dfrac{10y}{30}=\dfrac{15z}{30}\\ \Leftrightarrow\dfrac{x}{5}=\dfrac{y}{3}=\dfrac{z}{2}=\dfrac{x+y-z}{5+3-2}=\dfrac{90}{6}=15\\ \Leftrightarrow\left\{{}\begin{matrix}x=75\\y=45\\z=30\end{matrix}\right.\)
Tìm các số x, y, z biết:
a) \(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{5}=\dfrac{z}{4}\) và x + z - y = -49
b) \(\dfrac{x}{3}=\dfrac{y}{-2};\dfrac{x}{6}=\dfrac{z}{7}\) và 3x - z + 2y = 3
Lm hết nha mọi ngừi ^^
a: Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{12}=\dfrac{x-y+z}{10-15+12}=\dfrac{-49}{7}=-7\)
Do đó: x=-70; y=-135; z=-84
a: Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
a) \(\left\{{}\begin{matrix}\dfrac{x}{2}=\dfrac{y}{3}\\\dfrac{y}{5}=\dfrac{z}{4}\end{matrix}\right.\)
\(\Rightarrow\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{12}=\dfrac{x+z-y}{10+12-15}=-\dfrac{49}{7}=-7\)
\(\Rightarrow\left\{{}\begin{matrix}x=\left(-7\right).10=-70\\y=\left(-7\right).15=-105\\z=\left(-7\right).12=-84\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\dfrac{x}{3}=\dfrac{y}{-2}\\\dfrac{x}{6}=\dfrac{z}{7}\end{matrix}\right.\)
\(\Rightarrow\dfrac{x}{6}=\dfrac{y}{-4}=\dfrac{z}{7}=\dfrac{3x}{18}=\dfrac{2y}{-8}=\dfrac{3x-z+2y}{18-7-8}=\dfrac{3}{3}=1\)
\(\Rightarrow\left\{{}\begin{matrix}x=1.6=6\\y=1.\left(-4\right)=-4\\z=1.7=7\end{matrix}\right.\)
Tìm x, y, z biết:
\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\) và \(5z-3x-4y=50\)
Áp dụng t/c dtsbn:
\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}=\dfrac{3x-3}{6}=\dfrac{4y+12}{16}=\dfrac{5z-25}{30}=\dfrac{-3x+3-4y-12+5z-25}{-6-16+30}=\dfrac{50+3-12-25}{8}=\dfrac{16}{8}=2\\ \Rightarrow\left\{{}\begin{matrix}x-1=4\\y+3=8\\z-5=12\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=5\\y=5\\z=17\end{matrix}\right.\)
Tìm x,y,z biết:\(\dfrac{x-1}{2}\)=\(\dfrac{y+3}{4}\)=\(\dfrac{z-5}{6}\) và 5z-3x-4y=50
Tìm x,y biết :
6) 3x=4y và 2x + 3y = 7
7) \(\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{z}{7}\) và x-y+z=36
8) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{6}\) và 3x-2y+2z = 24
7) vì \(\dfrac{x}{5}\)=\(\dfrac{y}{6}\)=\(\dfrac{z}{7}\)và x-y+z=36
Nên theo tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{5}\)=\(\dfrac{y}{6}\)=\(\dfrac{z}{7}\)=\(\dfrac{x-y+z}{5-6+7}\)=\(\dfrac{36}{6}\)=6
\(\Rightarrow\)x=6.5=30
y=6.6=36
z=6.7=42
vậy x=30,y=36,z=42
Tìm hai số x,y biết
a/\(\dfrac{x^3}{8}=\dfrac{y^3}{27}=\dfrac{z^3}{64};x^2+2y^2-3z^2=-650\)
b/\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6};5z-3x-4y=50\)
b: Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}=\dfrac{-3x-4y+5z+3-12-25}{-3\cdot2-4\cdot4+5\cdot6}=\dfrac{16}{8}=2\)
Do đó: x=5; y=5; z=17
\(a,\dfrac{x^3}{8}=\dfrac{y^3}{27}=\dfrac{z^3}{64}\Rightarrow\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\Rightarrow\dfrac{x^2}{4}=\dfrac{y^2}{9}=\dfrac{z^2}{16}\)
Áp dụng t/c dtsbn:
\(\dfrac{x^2}{4}=\dfrac{y^2}{9}=\dfrac{z^2}{16}=\dfrac{x^2+2y^2-3z^2}{4+18-48}=\dfrac{-650}{-26}=25\\ \Rightarrow\left\{{}\begin{matrix}x^2=100\\y^2=225\\z^2=400\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\pm10\\y=\pm15\\z=\pm20\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)\) có giá trị là hoán vị của \(\left(\pm10;\pm15;\pm20\right)\)
Tìm x, y, z, t ∈ Z biết:
a, \(\dfrac{5}{x}=\dfrac{-10}{12}\) b, \(\dfrac{4}{-6}=\dfrac{x+3}{9}\) c, \(\dfrac{x-1}{25}=\dfrac{4}{x-1}\) d, \(\dfrac{x+1}{y}=\dfrac{-3}{5}\)
e, \(\dfrac{-12}{6}=\dfrac{x}{5}=\dfrac{-y}{3}=\dfrac{Z}{-17}=\dfrac{-t}{-9}\)
h, \(\dfrac{-24}{-6}=\dfrac{x}{3}=\dfrac{4}{y^2}=\dfrac{Z^3}{-2}\)
a) \(\dfrac{5}{x}=\dfrac{-10}{12}.\Rightarrow x=-6.\)
b) \(\dfrac{4}{-6}=\dfrac{x+3}{9}.\Rightarrow x+3=-6.\Leftrightarrow x=-9.\)
c) \(\dfrac{x-1}{25}=\dfrac{4}{x-1}.\left(đk:x\ne1\right).\Leftrightarrow\dfrac{x-1}{25}-\dfrac{4}{x-1}=0.\)
\(\Leftrightarrow\dfrac{x^2-2x+1-100}{25\left(x-1\right)}=0.\Leftrightarrow x^2-2x-99=0.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=11.\\x=-9.\end{matrix}\right.\) \(\left(TM\right).\)
Tìm x,y,z biết:\(\dfrac{x-1}{2}\)=\(\dfrac{y+3}{4}\)=\(\dfrac{z-5}{6}\) và 5z-3x-4y=50.
giúp mình với mọi người.
Tìm x,y,z biết:
a) 3x=2y, 7y=5z và x-y+z=32
b) \(\dfrac{x}{2}\)=\(\dfrac{y}{3}\) và x.y=24
c)\(\dfrac{x-1}{2}\)=\(\dfrac{y-2}{3}\)=\(\dfrac{z-3}{4}\) và 2x+3y-z=50
d)\(\dfrac{x}{2}\)=\(\dfrac{y}{3}\)=\(\dfrac{z}{5}\) và x.y.z=810