Question

[Nguyễn Ngô Bảo Châu]

X -20/11x13 -20/13x15 -20/15x17 -.......-20/53x55 =3/11

Answer 1

[ST]

\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)

\(\Rightarrow x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)

Đặt S = \(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+....+\frac{20}{53.55}\)

\(=10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)\)

\(=10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)\)

\(=10\left(\frac{1}{11}-\frac{1}{55}\right)\)

\(=10\cdot\frac{4}{55}=\frac{8}{11}\)

Thay A vào đề bài,ta được:

\(x-\frac{8}{11}=\frac{3}{11}\)

\(x=\frac{3}{11}+\frac{8}{11}\)

\(x=1\)

Answer 2

[ST]

Đổi thay A thành thay S nha bạn