Question

[Xuân Nguyễn Thị]

\(\dfrac{x+1}{2022}\)+\(\dfrac{x+2}{2021}\)+.....+\(\dfrac{x+23}{2000}\)+23=0

Mọi người giúp mik vs ạ,mai mik phải nộp rồi ạ!

Answer 1

[Akai Haruma]

Lời giải:
PT $\Leftrightarrow (\frac{x+1}{2022}+1)+(\frac{x+2}{2021}+1)+...+(\frac{x+23}{2000}+1)=0$

$\Leftrightarrow \frac{x+2023}{2022}+\frac{x+2023}{2021}+...+\frac{x+2023}{2000}=0$

$\Leftrightarrow (x+2023)(\frac{1}{2022}+\frac{1}{2021}+...+\frac{1}{2000})=0$
Dễ thấy tổng trong () luôn dương 

$\Rightarrow x+2023=0$

$\Leftrightarrow x=-2023$