Question

[Nguyễn Lê Việt ANh]

giải các phương trình sau

\(\dfrac{x+1}{1998}+\dfrac{x+2}{1997}=\dfrac{x +3}{1996}+\dfrac{x+4}{1995}\)

Answer 1

[Mashiro Shiina]

Vào trang cá nhân của t mà xem.T vừa làm r.Lười gõ lại lắm T^T

Answer 2

[Song Thư]

\(\dfrac{x+1}{1998}+\dfrac{x+2}{1997}=\dfrac{x+3}{1996}+\dfrac{x+4}{1995}\)

\(=\dfrac{x+1}{1998}+\dfrac{x+2}{1997}-\dfrac{x+3}{1996}-\dfrac{x+4}{1995}=0\)

\(=\dfrac{x+1}{1998}+1+\dfrac{x+2}{1997}+1-\dfrac{x+3}{1996}-1-\dfrac{x+4}{1995}-1=0\)

\(=\dfrac{x+1999}{1998}+\dfrac{x+1999}{1998}-\left(\dfrac{x+3}{1996}+1\right)-\left(\dfrac{x+4}{1995}+1\right)=0\)

\(=\dfrac{x+1999}{1998}+\dfrac{x+1999}{1997}-\dfrac{x+1999}{1996}-\dfrac{x+1999}{1995}=0\)

\(=\left(x+1999\right)\left(\dfrac{1}{1998}+\dfrac{1}{1997}-\dfrac{1}{1996}-\dfrac{1}{1995}\right)=0\)

⇔\(x+1999=0\)

Vậy \(x=-1999\)