cho x/3=y/4 và y/5=z/6.tính M=2x+3y+4z/3x+4y+5z

Đáp án:

`⊛``x/3=y/4`

`-> x/15=y/20`               `(1)`

`⊛` `y/5=z/6`

`-> y/20=z/24`                `(2)`

`(1)(2) -> x/15=y/20=z/24`

Đặt : `x/15=y/20=z/24=k` 

`->x=15k;y=20k;z=24k` `(\ast)`

`M={2x+3y+4z}/{3x+4y+5z}` 

Thay `\ast` vào `M`

`-> M={2.15k+3.20k+4.24k}/{3.15k+4.20k+5.24k}`

`-> M ={30k+60k+96k}/{45k+80k+120k}`

`-> M ={186k}/{245k}`

`-> M = 186/245`

Answer

Ta có:

`x/3 = y/4 ; y/5 = z/6`

`=> x/3 . 1/5 = y/4 . 1/5 ; y/5 . 1/4 = z/6 . 1/4`

`=> x/15 = y/20 ; y/20 = z/24`

`=> x/15 = y/20 = z/24`

Đặt: `x/15 = y/20 = z/24 = k \ (k \in RR ; k \ne 0)`

`=>` `{(x = 15k),(y = 20k),(z = 24k):}`

Mà: `M = {2x + 3y + 4z}/{3x + 4y + 5z}`

`=> M = {2 . 15k + 3 . 20k + 4 . 24k}/{3 . 15k + 4 . 20k + 5 . 24k}`

`=> M = {30k + 60k + 96k}/{45k + 80k + 120k}`

`=> M = {90k + 96k}/{125k + 120k}`

`=> M = {186k}/{245k}`

`=> M = 186/245`

Vậy `M = 186/245` khi `x/3 = y/4 ; y/5 = z/6`