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Bài làm
\(\frac{3x}{2.5}+\frac{3x}{5.8}+\frac{3x}{8.11}+\frac{3x}{11.14}=\frac{1}{21}\)
\(\Leftrightarrow\frac{x}{2}-\frac{x}{5}+\frac{x}{5}-\frac{x}{8}+\frac{x}{8}-\frac{x}{11}+\frac{x}{11}-\frac{x}{14}=\frac{1}{21}\)
\(\Leftrightarrow\frac{x}{2}-\frac{x}{14}=\frac{1}{21}\)
\(\Leftrightarrow\frac{7x}{14}-\frac{x}{14}=\frac{1}{21}\)
\(\Leftrightarrow\frac{6x}{14}=\frac{1}{21}\)
\(\Leftrightarrow126x=14\)
\(\Leftrightarrow x=\frac{1}{9}\)
Học tôt
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\(\frac{1}{2}-\frac{1}{14}=\frac{3}{7}\). Mà ở đây kết quả là \(\frac{1}{21}\)nên phân số phải nhóm ra ngoài là:
\(\frac{1}{21}:\frac{3}{7}=\frac{1}{9}\). Ta có:
\(\frac{1}{9}.\left(\frac{3x}{2.5}+\frac{3x}{5.8}+\frac{3x}{8.11}+\frac{3x}{11.14}\right)=\frac{1}{21}\). Suy ra 3x=9. Vậy x=3
Nhầm nha: Vì có 3x nên phân số nhóm ra ngoài là \(\frac{1}{3}\). Ta có tương tự. Suy ra 3x=3. Vậy x=1
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x. [3/2.5 +3/5.8+ 3/8.11+3/11.14] = 1/21
=> x . [1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14] = 1/21
=> x. [1/2-1/14] = 1/21 => x . 3/7= 1/21
=> x = 1/9
x. [3/2.5 +3/5.8+ 3/8.11+3/11.14] = 1/21
=> x . [1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14] = 1/21
=> x. [1/2-1/14] = 1/21 => x . 3/7= 1/21
=> x = 1/9
mình nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
\(7\frac{x}{2.5}+7\frac{x}{5.8}+.....+7.\frac{x}{17.20}=\frac{21}{10}\)
\(7\left(\frac{x}{2.5}+\frac{x}{5.8}+...+\frac{x}{17.20}\right)=\frac{21}{10}\)
\(\frac{x}{2.5}+\frac{x}{5.8}+...+\frac{x}{17.20}=\frac{21}{70}\)
\(\frac{x.3}{2.5.3}+\frac{x.3}{5.8.3}+...+\frac{x.3}{17.20.3}=\frac{21}{70}\)
\(x.\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{17.20}\right)=\frac{21}{70}\)
\(x.\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{20}\right)=\frac{21}{70}\)
\(x.\frac{1}{3}.\frac{9}{20}=\frac{21}{70}\)
=> \(x=2\)
\(x=\frac{7x}{2}\)\(-\frac{7x}{5}+\)\(\frac{7x}{5}\)\(-\frac{7x}{8}\)\(+\frac{7x}{8}\)\(-\frac{7x}{11}\)\(+\frac{7x}{11}\)\(-\frac{7x}{14}\)\(+\frac{7x}{14}\)\(-\frac{7x}{17}+\)\(\frac{7x}{17}\)\(-\frac{7x}{20}\)\(=\frac{21}{10}\)
\(x=\frac{7x}{2}\)\(-\frac{7x}{20}\)\(=\frac{21}{10}\)
\(x=\frac{7x.10}{20}\)\(+\frac{7x}{20}\)\(=\frac{21}{10}\)
\(x=\frac{7x.10+7x}{20}\)\(=\frac{21}{10}\)
\(x=\frac{7x.\left(10+2\right)}{20.2}\)\(=\frac{7x.12}{40}\)\(=\frac{21}{10}\)
\(=>\frac{7x.12:4}{40:4}=\)\(\frac{21}{10}\)
\(=>x=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{3}.\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right]\)
\(\frac{1}{3}\left[\frac{1}{2}-\frac{1}{20}\right]=\frac{1}{3}.\frac{9}{20}=\frac{3}{20}\)
mk đầu tiên đó
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{14.17}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{14}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)\(< \frac{17}{34}=\frac{1}{2}\)
\(\Rightarrow\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{14.17}< \frac{1}{2}\)
Vậy:..........................................(đpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
xét vế trái
ta có:đề\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{14}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}< < \frac{1}{2}\)
vậy vế trái bé hơn \(\frac{1}{2}\)
P/S: \(< < \)là luôn luôn bé hơn nha
k mình nha bạn
Thiengl2015#
Ta có :
\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{14.17}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{14}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}\)
Mà \(\frac{1}{2}-\frac{1}{17}< \frac{1}{2}\)
Nên \(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{14.17}< \frac{1}{2}\left(đpcm\right)\)
\(\frac{3x}{2\cdot5}+\frac{3x}{5\cdot8}+.........+\frac{3x}{14\cdot17}=\frac{1}{21}\)
\(\Rightarrow3x\cdot\left(\frac{1}{2\cdot5}+\frac{1}{5\cdot7}+........+\frac{1}{14\cdot17}\right)=\frac{1}{21}\)
\(\Rightarrow3x\cdot\left[\frac{1}{3}\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot7}+......+\frac{3}{14\cdot17}\right)\right]=\frac{1}{21}\)
\(\Rightarrow3x\cdot\left[\frac{1}{3}\cdot\left(\frac{1}{2}-\frac{1}{17}\right)\right]=\frac{1}{21}\)
\(\Rightarrow3x\cdot\left(\frac{1}{3}\cdot\frac{15}{34}\right)=\frac{1}{21}\)
\(\Rightarrow3x\cdot\frac{5}{34}=\frac{1}{21}\)\(\Rightarrow x=\frac{1}{21}:\frac{1}{34}:3\)
\(\Rightarrow x=\frac{34}{315}\)
ai k mh mh k lại
k cho mh nha