Đáp án:
`(x - 1)/2 = (y-2)/3 = (z-3)/4`
`⇔ (x- 1)/2 = (2 (y - 2) )/(3 × 2) = (3 (z - 3) )/(4 × 3)`
`⇔ (x-1)/2 = (2y - 4)/6 = (3z - 9)/12`
Áp dụng tính chất dãy tỉ số bằng nhau có :
`(x-1)/2 = (2y - 4)/6 = (3z - 9)/12 = ( (x-1) - (2y - 4) + (3z - 9) )/(2 - 6 + 12) = (x-1 - 2y + 4 + 3z - 9)/8 = ( (x - 2y + 3z) + (-1 + 4 - 9) )/8 = (14 - 6)/8 = 8/8 = 1`
`⇔` \(\left\{ \begin{array}{l}\dfrac{x-1}{2}=1\\ \dfrac{2y-4}{6}=1\\ \dfrac{3z - 9}{12}=1\end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}x-1=2×1\\ 2y-4=6×1\\3z-9=12×1\end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}x-1=2\\2y-4=6\\3z-9=12\end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}x=2 +1\\2y=10\\3z=21\end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}x=3\\y=5\\z=7\end{array} \right.\)
Vậy `(x;y;z) = (3;5;7)`
