-Nếu |x-2013|-2014=2015->|x-2013| = 4029
+ Nếu x-2013 =4029 -> x= 6042
+ Nếu x-2013 = -4029 -> x = -2016
- Nếu |x-2013|-2014= -2015 -> |x-2013| = -1 (loại vì |x-2013| \(\ge\)0 )
Vậy x= 6042 ; x=-2016 là các giá trị cần tìm.
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
=> \(x-\left(20\times\frac{1}{11.13}+20\times\frac{1}{13.15}+20\times\frac{1}{15.17}+...+20\times\frac{1}{53.55}\right)=\frac{3}{11}\)
\(x-20\times\left(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{53.55}\right)=\frac{3}{11}\)
\(x-20\times\left(\frac{1}{2}\times\left(\frac{1}{11}-\frac{1}{13}\right)+\frac{1}{2}\times\left(\frac{1}{13}-\frac{1}{15}\right)+\frac{1}{2}\times\times+...+\frac{1}{2}\times\left(\frac{1}{53}-\frac{1}{55}\right)\right)=\frac{3}{11}\)
\(x-20\times\frac{1}{2}\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-...-\frac{1}{53}+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10\times\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10\times\frac{4}{55}=\frac{3}{11}\)
\(x-\frac{10}{11}=\frac{3}{11}\)
=> \(x=\frac{3}{11}+\frac{10}{11}=\frac{13}{11}\)
Vậy x=\(\frac{13}{11}\)