Question

GIẢI PHƯƠNG TRÌNH

\(\frac{x-1001}{1002}+\frac{x-1950}{53}=\frac{x+158}{2161}+\frac{x+193}{2196}\)

Answer 1

Lời giải:

$\frac{x-1001}{1002}+\frac{x-1950}{53}=\frac{x+158}{2161}+\frac{x+193}{2196}$

$\Leftrightarrow \frac{x-1001}{1002}-1+\frac{x-1950}{53}-1=\frac{x+158}{2161}-1+\frac{x+193}{2196}-1$

$\Leftrightarrow \frac{x-2003}{1002}+\frac{x-2003}{53}=\frac{x-2003}{2161}+\frac{x-2003}{2196}$

$\Leftrightarrow (x-2003)\left(\frac{1}{1002}+\frac{1}{53}-\frac{1}{2161}-\frac{1}{2196}\right)=0$

Dễ thấy $\left(\frac{1}{1002}+\frac{1}{53}-\frac{1}{2161}-\frac{1}{2196}\right)\neq 0$ nên $x-2003=0\Rightarrow x=2003$