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\(xy+3x-7y=23\)
\(\Leftrightarrow x\left(y+3\right)-7y-21=2\)
\(\Leftrightarrow x\left(y+3\right)-7\left(y+3\right)=2\)
\(\Leftrightarrow\left(x-7\right)\left(y+3\right)=2=1.2=2.1=\left(-1\right).\left(-2\right)=\left(-2\right).\left(-1\right)\)
Lập bảng:
| \(x-7\) | \(1\) | \(2\) | \(-1\) | \(-2\) |
| \(y+3\) | \(2\) | \(1\) | \(-2\) | \(-1\) |
| \(x\) | \(8\) | \(9\) | \(6\) | \(5\) |
| \(y\) | \(-1\) | \(-2\) | \(-5\) | \(-4\) |
Vậy \(\left(x,y\right)\in\left\{\left(8,-1\right);\left(9,-2\right);\left(6,-5\right);\left(5,-4\right)\right\}\)
\(\left(1-\frac{1}{1931}\right)\left(1-\frac{1}{1932}\right)......\left(1-\frac{1}{2012}\right)\)
\(=\frac{1930}{1931}\cdot\frac{1931}{1932}\cdot...\cdot\frac{2011}{2012}\)
\(=\frac{1930\cdot1931\cdot...\cdot2011}{1931\cdot1932\cdot...\cdot2012}=\frac{1930}{2012}=\frac{965}{1006}\)
\(\left(1-\frac{1}{1931}\right)\times\left(1-\frac{1}{1932}\right)\times\left(1-\frac{1}{1933}\right)\times...\times\left(1-\frac{1}{2012}\right)\)
\(=\left(\frac{1931}{1931}-\frac{1}{1931}\right)\times\left(\frac{1932}{1932}-\frac{1}{1932}\right)\times\left(\frac{1933}{1933}-\frac{1}{1933}\right)\times...\times\left(\frac{2012}{2012}-\frac{1}{2012}\right)\)
\(=\frac{1930}{1931}\times\frac{1931}{1932}\times\frac{1932}{1933}\times...\times\frac{2011}{2012}\)
\(=\frac{1930\times1931\times1932\times...\times2011}{1931\times1932\times1933\times...\times2012}\)
\(=\frac{1930}{2012}=\frac{965}{1006}\)
1) So sánh
3 77/379 và 3 79/381
2)
A= 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36
Giúp mình nhé❤❤❤❤❄▫〰▫▫▫▫▫▫
2) A = \(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{2}\).\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}\right)\)
=> \(\frac{1}{2}\).A = \(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{3}-\frac{1}{9}\)
=> \(\frac{1}{2}\).A = \(\frac{2}{9}\)
=> A = \(\frac{2}{9}:\frac{1}{2}\)
=> A = \(\frac{4}{9}\)
trả lời
Câu hỏi của Nguyễn Ngọc Thảo My - Toán lớp 5 - Học toán với OnlineMath
vào thống kê !!!
Ta có : \(N=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1000.1001}\)
\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{1001-1000}{1000.1001}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1000}-\frac{1}{1001}\)
\(=1-\frac{1}{1001}=\frac{1000}{1001}\)
Ta thấy : \(1001< 2020\Rightarrow\frac{1}{1001}>\frac{1}{2020}\)
\(\Rightarrow-\frac{1}{1001}< -\frac{1}{2020}\)
\(\Rightarrow1-\frac{1}{1001}< 1-\frac{1}{2020}\Rightarrow\frac{1000}{1001}< \frac{2019}{2020}\)
Hay : \(N< M\)
\(C=\left(1-\frac{1}{1931}\right)\left(1-\frac{1}{1932}\right)\left(1-\frac{1}{1933}\right).....\left(1-\frac{1}{2019}\right)\)
\(C=\frac{1930}{1931}\cdot\frac{1931}{1932}\cdot\frac{1932}{1933}\cdot\cdot\cdot\cdot\cdot\frac{2018}{2019}\)
\(C=\frac{1930\cdot1931\cdot1932\cdot\cdot\cdot\cdot\cdot2018}{1931\cdot1932\cdot1933\cdot\cdot\cdot\cdot\cdot2019}=\frac{1930}{2019}\)
(1-1/1931).(1-1/1932).(1-1/1933).........(1-1/2019)
= (1930/1931).(1931/1932).(1932/1933)......(2018/(2019)
= 1930/2019
@ Hc tốt nha cj !!!!
C=\(\left(1-\frac{1}{1931}\right).\left(1-\frac{1}{1932}\right).\left(1-\frac{1}{1933}\right)...........\left(1-\frac{1}{2019}\right)\)
C=\(\left(\frac{1931-1}{1931}\right).\left(\frac{1932-1}{1932}\right).\left(\frac{1933-1}{1933}\right).......\left(\frac{2019-1}{2019}\right)\)
C=\(\frac{1930}{1931}.\frac{1931}{1932}.\frac{1932}{1933}...............\frac{2018}{2019}\)
C=\(\frac{1930.1931.1932.............2018}{1931.1932.1933................2019}\)
C=\(\frac{1930}{2019}\)
Vậy C=\(\frac{1930}{2019}\)
Chúc bn học tốt