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\(-56+\left|-x+23\right|=-41\)
\(\Leftrightarrow-56+\left|23-x\right|=-41\)
\(\Leftrightarrow\left|23-x\right|-56=-41\)
\(\Leftrightarrow\left|23-x\right|=15\)
\(\Leftrightarrow\orbr{\begin{cases}23-x=15\\23-x=-15\end{cases}\Leftrightarrow\orbr{\begin{cases}x=8\\x=38\end{cases}}}\)
Vậy \(x\in\left\{8;38\right\}\)
-56+|-x+23|=-41
|-x+23|=-41- (-56)
|-x+23|=-41+56
|-x+23|=15
=> \(\orbr{\begin{cases}-x+23=15\\-x+23=-15\end{cases}}\)
=>\(\orbr{\begin{cases}-x=15-23\\-x=-15-23\end{cases}}\)
=>\(\orbr{\begin{cases}-x=-8\\-x=-38\end{cases}}\)
=>\(\orbr{\begin{cases}x=8\\x=38\end{cases}}\)
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\(=1-\dfrac{1}{2}+1-\dfrac{1}{6}+...+1-\dfrac{1}{90}\)
\(=10-\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\right)\)
\(=10-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
=9+1/10
=9,1
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a) \(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)
\(=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+1-\frac{1}{56}+1-\frac{1}{72}+1-\frac{1}{90}\)
\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)
\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(=8-\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+\frac{9-8}{8.9}+\frac{10-9}{9.10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)=7,6\)
b) Bạn làm tương tự.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)
\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{38}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
720 : [ 41 - ( 56 : x - 5 ) ] = 40
41 - ( 56 : x - 5 ) = 720 : 40
41 - ( 56 : x - 5 ) = 18
56 : x - 5 = 41 - 18
56 : x - 5 = 23
56 : x = 23 + 5
56 : x = 28
x = 56 : 28
x = 2
41 . 56 - 141 . 56 + 300 . 56
= 56 . ( 41 - 141 + 300 )
= 56 . 200
= 11200
kết quả là:
11 200
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