Đáp án:
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`1,`
Đặt `x/2 = y/3 = z/5 = k`
`↔` \(\left\{ \begin{array}{l}\dfrac{x}{2}=k\\ \dfrac{y}{3}=k\\ \dfrac{z}{5}=k\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=2k\\y=3k\\z=5k\end{array} \right.\)
Có : `A = (3x-y + 5x)/(x+y+3x)`
Thay \(\left\{ \begin{array}{l}x=2k\\y=3k\\z=5k\end{array} \right.\) vào `A` ta được :
`↔ A = (3 (2k) - 3k +5 (2k) )/(2k + 3k + 3 (2k) )`
`↔ A = (6k - 3k + 10k)/(2k + 3k + 6k)`
`↔ A = (k(6-3 +10) )/(k (2+3+6) )`
`↔ A = (6-3+10)/(2+3+6)`
`↔ A = (3+10)/(5+6)`
`↔A = 13/11`
Vậy `A = 13/11` khi `x/2=y/3=z/5`
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`2,`
Đặt `x/4 = y/7 = z/5 = k`
`↔` \(\left\{ \begin{array}{l}\dfrac{x}{4}=k\\ \dfrac{y}{7}=k\\ \dfrac{z}{5}=k\end{array} \right.\)
`↔` \(\left\{ \begin{array}{l}x=4k\\y=7k\\z=5k\end{array} \right.\)
Có : `B = (2x + y - z)/(x+6y - 5z)`
Thay \(\left\{ \begin{array}{l}x=4k\\y=7k\\z=5k\end{array} \right.\) vào `B` ta được :
`↔ B = (2 (4k) + 7k - 5k)/(4k + 6 (7k) - 5 (5k) )`
`↔ B = (8k + 7k-5k)/(4k + 42k - 25k)`
`↔ B = (k (8+7-5) )/(k (4+42-25) )`
`↔ B=(8+7-5)/(4+42-25)`
`↔ B = (15 - 5)/(46 - 25)`
`↔ B = 10/21`
Vậy `B=10/21` khi `x/4=y/7=z/5`
