Ta có : \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)
=> \(\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}\)
- Áp dụng tính chất dãy tỉ số bằng nhau ta được :
\(\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}=\frac{5x-5-3y-9-4z+20}{10-12-24}=\frac{5x-3y-4z+6}{-26}=\frac{46+6}{-26}=-2\)
=> \(\left\{{}\begin{matrix}5x-5=-20\\3y+9=-24\\4z-20=-48\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}5x=-15\\3y=-33\\4z=-28\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}x=-3\\y=-11\\z=-7\end{matrix}\right.\)
Vậy x,y,z có giá trị lần lượt là -3,-11,-7 .
\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\Rightarrow\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}\)
-Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}=\frac{\left(5x-3y-4z\right)-\left(5+9-20\right)}{10-12-24}=\frac{46+6}{-26}=\frac{52}{-16}=-2\)
Do đó:
\(\frac{5x-5}{10}=-2\Leftrightarrow\frac{x-1}{2}=-2\Rightarrow x-1=-4\Rightarrow x=-3\)
\(\frac{3y+9}{12}=-2\Leftrightarrow\frac{y+3}{4}=-2\Rightarrow y+3=-8\Rightarrow y=-11\)
\(\frac{4z-20}{24}=-2\Leftrightarrow\frac{z-5}{6}=-2\Rightarrow z-5=-12\Rightarrow x=-7\)
Vậy x = -3; y = -11; z = -7
Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\Leftrightarrow\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}=\frac{\left(5x-3y-4z\right)-\left(5+9-20\right)}{10-12-24}=\frac{46+6}{22}=\frac{26}{11}\)
\(\Rightarrow\left\{{}\begin{matrix}5x-5=\frac{260}{11}\\3y+9=\frac{312}{11}\\4z-20=\frac{624}{11}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\frac{63}{11}\\y=\frac{71}{11}\\z=\frac{211}{11}\end{matrix}\right.\)
