$\frac{x+19}{2019}$ $\frac{x+18}{2018}$ $\frac{x+17}{2017}$ +…..+ $\frac{x+1}{2001}$ =19

0 bình luận về “$\frac{x+19}{2019}$ $\frac{x+18}{2018}$ $\frac{x+17}{2017}$ +…..+ $\frac{x+1}{2001}$ =19”

1. Đáp án + Giải thích các bước giải:

   `(x+19)/2019 + (x+18)/2018 + (x+17)/2017 + … + (x+1)/2001 = 19`

   `to (x+19)/2019 + (x+18)/2018 + (x+17)/2017 + … + (x+1)/2001 – 19 = 0`

   `to ( (x+19)/2019 – 1 ) + ( (x+18)/2018 – 1 ) + ( (x+17)/2017 – 1 ) + … + ( (x+1)/2001 – 1 ) = 0 `

   `to (x+19-2019)/2019 + (x+18-2018)/2018 + (x+17-2017)/2017 + … + (x+1-2001)/2001 = 0`

   `to (x-2000)/2019 + (x-2000)/2018 + (x-2000)/2017 + … + (x-2000)/2001 = 0`

   `to (x-2000) . (1/2019+1/2018+1/2017+…+1/2001)=0`

   Mà `1/2019+1/2018+1/2017+…+1/2001 ne 0`

   `to x-2000=0`

   `to x=2000`

   Vậy `x=2000`

    

   Trả lời

2. (x+19/2019 – 1)+(x+18/2018 – 1)+(x+2017/2017 – 1)+…+(x+1/2001 – 1)=0 (Đổi 19 sang vế trái)

   => x-2000/2019 + x-2000/2018 + x-2000/2017+…+  x-2000/2001 =0

   nhóm nhân tử chung x-2000:

   => (x-2000)*(1/2019 +1/2018 +1/2017+…+ 1/2001)=0

   vì 1/2019+1/2018+1/2017+…+1/2001 >0

   =>x-2000=0

   =>x=2000

    

   Trả lời