Đáp án:
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Có : `x/y = 3/2`
`↔ x/3 = y/2`
`↔ x/15 = y/10` `(1)`
Có : `y/z = 5/7`
`↔ y/5 = z/7`
`↔ y/10 = z/14` `(2)`
Từ `(1), (2)`
`↔ x/15 = y/10 = z/14`
`↔ x/15 = (3y)/30 = (2z)/28`
Có : `|x + 3y - 2z| = 17`
`↔` \(\left[ \begin{array}{l}x+ 3y - 2z = 17\\x+3y - 2z=-17\end{array} \right.\)
$\bullet$ Khi `x + 3y - 2z = 17`
Áp dụng tính chất dãy tỉ số bằng nhau có :
`x/15 = (3y)/30 = (2z)/28 = (x + 3y - 2z)/(15 + 30 - 28) = 17/17 = 1`
`↔` \(\left\{ \begin{array}{l}\dfrac{x}{15}=1\\ \dfrac{3y}{30}=1\\ \dfrac{2z}{28}=1\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=15×1\\3y=30×1\\2z=28×1\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=15\\ 3y = 30\\2z=28\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=15\\y=30÷3\\z=28÷2\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=15\\y=10\\z=14\end{array} \right.\)
$\bullet$ Khi `x + 3y - 2z=-17`
Áp dụng tính chất dãy tỉ số bằng nhau có :
`x/15 = (3y)/30 = (2z)/28 = (x + 3y - 2z)/(15 + 30 - 28) = (-17)/17 = -1`
`↔` \(\left\{ \begin{array}{l}\dfrac{x}{15}=-1\\ \dfrac{3y}{30}=-1\\ \dfrac{2z}{28}=-1\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=15×(-1)\\3y=30×(-1)\\2z=28×(-1)\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=-15\\ 3y = -30\\2z=-28\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=-15\\y=-30÷3\\z=-28÷2\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=-15\\y=-10\\z=-14\end{array} \right.\)
Vậy `(x;y;z) = (15;10;14), (-15;-10;-14)`
