Question

Biết \(x>1,\)tìm tất cả các giá trị của \(x\)đáp ứng biểu thức sau:

\(\frac{x-2017}{2018}-\frac{x-2018}{2017}=\frac{2017}{x-2018}-\frac{2018}{x-2017}\)

Answer 1

\(\frac{x-2017}{2018}-\frac{x-2018}{2017}=\frac{2017}{x-2018}-\frac{2018}{x-2017}\)

\(\Leftrightarrow\)\(\frac{2017\left(x-2017\right)-2018\left(x-2018\right)}{2017.2018}=\frac{2017\left(x-2017\right)-2018\left(x-2018\right)}{\left(x-2017\right)\left(x-2018\right)}\)

Do \(2017\left(x-2017\right)-2018\left(x-2018\right)\ne0\) nên \(\left(x-2017\right)\left(x-2018\right)=2017.2018\)

\(\Leftrightarrow\)\(x^2-4035x+2017.2018=2017.2018\)

\(\Leftrightarrow\)\(x\left(x-4035\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\left(l\right)\\x=4035\left(n\right)\end{cases}}\)

Vậy x = 4035