Question

tìm x biết:

b)\(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}-x+\frac{23}{231}=\frac{5}{77}\)

Answer 1

Đặt  \(A=\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\)

      \(A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{19}-\frac{1}{21}\)

       \(A=\frac{1}{11}-\frac{1}{21}=\frac{10}{231}\)

thay A vào ta được:

\(\frac{10}{231}-x+\frac{23}{231}=\frac{5}{77}\) 

\(x+\frac{23}{231}=\frac{10}{231}-\frac{5}{77}=-\frac{5}{231}\)

\(x=-\frac{5}{231}-\frac{23}{231}=\frac{-4}{33}\)

Answer 2

\(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}-x+\frac{23}{231}=\frac{5}{77}\)\(\frac{5}{77}\)

=>\(\frac{1}{11}-\frac{1}{21}-x+\frac{23}{231}=\frac{5}{77}\)

=>\(\frac{10}{231}+\frac{23}{231}-x=\frac{5}{77}\)

=>\(\frac{33}{231}-x=\frac{5}{77}\)

=>\(\frac{1}{7}-x=\frac{5}{77}\)

=>\(\frac{11}{77}-x=\frac{5}{77}\)

=>\(x=\frac{11}{77}-\frac{5}{77}=\frac{6}{77}\)

Vậy \(x=\frac{6}{77}\)