Question

(\(\frac{2}{11x13}\)+\(\frac{2}{13x15}\)+\(\frac{2}{15x17}\)+\(\frac{2}{17x19}\)+\(\frac{2}{19x21}\)) x 462 - x = 19

Answer 1

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right)\cdot462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)\cdot462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)

\(\Rightarrow\frac{10}{231}\cdot462-x=19\)

\(\Rightarrow20-x=19\Rightarrow x=1\)

Answer 2

Ta có:

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right).462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right).462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right).462-x=19\)

\(\Rightarrow\frac{10}{231}.462-x=19\Leftrightarrow20-x=19\)

\(\Rightarrow x=20-19=1\)