Question

1/Tìm x, biết:

          (2/11.13 + 2/13.15 +...+ 2/19.21) - x + 4 + 221/231 = 7/3

                                             

 

Answer 1

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4=\frac{7}{3}-\frac{221}{231}\)

\(\left(\frac{1}{11}-\frac{1}{21}\right)-x+4=\frac{106}{77}\)

\(\frac{10}{231}-x=\frac{106}{77}-4\)

\(\frac{10}{231}-x=-\frac{202}{77}\)

\(x=\frac{10}{231}-\left(-\frac{202}{77}\right)\)

\(x=\frac{8}{3}\)

Answer 2

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\frac{10}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\frac{10}{231}-x+4=\frac{7}{3}-\frac{221}{231}\)

\(\frac{10}{231}-x+4=\frac{106}{77}\)

\(\frac{10}{231}-x=\frac{106}{77}-4\)

\(\frac{10}{231}-x=\frac{-202}{77}\)

\(x=\frac{10}{231}-\frac{-202}{77}\)

\(x=\frac{8}{3}\)