Ta có :
\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{1}\)
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{1}\)
Đặt \(A=\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\)
\(A=10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)\)
\(A=10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)\)
\(A=10\left(\frac{1}{11}-\frac{1}{55}\right)\)
\(A=10.\frac{4}{55}=\frac{40}{55}=\frac{8}{11}\)
\(\Rightarrow x-\frac{8}{11}=\frac{3}{1}=3\)
\(x=3+\frac{8}{11}=\frac{33}{11}+\frac{8}{11}=\frac{41}{11}\)
Ủng hộ mk nha !!! ^_^
><in lỗi bn, 3/11 chứ k phải \(\frac{3}{1}\)
Ta có \(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(\text{Đ}\text{ặt}:A=\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\)
\(A=\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\)
\(A=10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)\)
\(A=10\left(\frac{1}{11}-\frac{1}{55}\right)\)
\(A=10\left(\frac{1}{11}-\frac{1}{55}\right)\)
\(\Rightarrow x-\frac{8}{11}=\frac{3}{11}\)
\(=>x=1\)
