Đáp án:
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Có : `2x = 4y = 5z`
`↔ (2x)/20 = (4y)/20 = (5z)/20`
`↔ x/10 = y/5 = z/4`
`↔ (2x)/20 = (3y)/15 = z/4`
Áp dụng tính chất dãy tỉ số bằng nhau có :
`(2x)/20 = (3y)/15 = z/4 = (2x - 3y - z)/(20-15-4) = 1/1 = 1`
`↔` \(\left\{ \begin{array}{l}\dfrac{2x}{20}=1\\ \dfrac{3y}{15}=1\\ \dfrac{z}{4}=1\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}2x=20×1\\3y=15×1\\z=4×1\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}2x=20\\3y=15\\z=4\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=20÷2\\y=15÷3\\z=4\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=10\\y=5\\z=4\end{array} \right.\)
Vậy `(x;y;z) = (10;5;4)`
