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LA
3 tháng 3 2018
\(\frac{x}{6}+\frac{x}{10}+\frac{x}{15}+\frac{x}{21}+\frac{x}{28}+\frac{x}{36}+\frac{x}{45}+\frac{x}{55}+\frac{x}{66}+\frac{x}{78}+\frac{x}{78}=\frac{220}{39}\)
\(\Leftrightarrow x\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}+\frac{1}{66}+\frac{1}{78}+\frac{1}{78}\right)=\frac{220}{39}\)
\(\Leftrightarrow x\cdot\frac{20}{39}=\frac{220}{39}\Rightarrow x=11\)
3 tháng 3 2018
\(\frac{x}{6}+\frac{x}{10}+\frac{x}{15}+\frac{x}{21}+\frac{x}{28}+\frac{x}{36}+\frac{x}{45}+\frac{x}{55}+\frac{x}{66}+\frac{x}{78}+\frac{x}{78}=\frac{220}{39}\)
\(=>x=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}+\frac{1}{66}+\frac{1}{78}+\frac{1}{78}=\frac{220}{39}\)
\(x\cdot\frac{20}{39}=\frac{220}{39}\)
\(x=\frac{220}{39}:\frac{20}{39}=11\)
17 tháng 4 2018
\(\dfrac{x}{6}+\dfrac{x}{10}+\dfrac{x}{15}+........+\dfrac{x}{78}=\dfrac{220}{39}\)
\(\Leftrightarrow\dfrac{2x}{12}+\dfrac{2x}{20}+........+\dfrac{2x}{156}=\dfrac{220}{39}\)
\(\Leftrightarrow2x\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+..........+\dfrac{1}{12.13}\right)=\dfrac{220}{39}\)
\(\Leftrightarrow2x\left(\dfrac{1}{3}-\dfrac{1}{13}\right)=\dfrac{220}{39}\)
\(\Leftrightarrow2x.\dfrac{10}{39}=\dfrac{220}{39}\)
\(\Leftrightarrow x.\dfrac{20}{39}=\dfrac{220}{39}\)
\(\Leftrightarrow x=11\)
Vậy ...
17 tháng 4 2017
Gọi biểu thức là A
\(A=\dfrac{2x}{12}+\dfrac{2x}{20}+\dfrac{2x}{30}+....+\dfrac{2x}{156}=\dfrac{200}{39}\)
Ta có công thức :
\(\dfrac{a}{b.c}=\dfrac{a}{c-b}.\left(\dfrac{1}{b}-\dfrac{1}{c}\right)\)
Áp dụng công thức trên, ta có :
\(A=\dfrac{2x}{3.4}+\dfrac{2x}{4.5}+\dfrac{2x}{5.6}+....+\dfrac{2x}{12.13}\)
\(A=2x.\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+....+\dfrac{1}{12}-\dfrac{1}{13}\right)\)
\(A=2x.\left(\dfrac{1}{3}-\dfrac{1}{13}\right)\)
\(A=2x.\left(\dfrac{10}{39}\right)=\dfrac{200}{39}\)
\(A=2x=\dfrac{200}{39}:\dfrac{10}{39}\)
\(2x=20\)
\(\Rightarrow x=10\)
mink nghĩ vậy bạn ạ
NT
0
DT
0
PT
1
22 tháng 4 2018
(x/6+x/10+...+x/66+x/78)*2=220/39*2
x/12+x/20+...x/132+x/156=440/39
x/2-x/3+x/3-x/4+...+x/11-x/12+x/12-x/13=440/39
x/2-x/13=440/39
11x/26=440/39
33x/78=880/78
33x=880
x=880/33
x=80/3=26, (6)
PH
Tìm x biết : \(\frac{1}{45}+\frac{1}{55}+\frac{1}{66}+...+\frac{2}{x.\left(x+1\right)}=\frac{1}{9}\)
1
23 tháng 4 2016
\(\frac{1}{45}+\frac{1}{55}+\frac{1}{66}+...+\frac{2}{x.\left(x+1\right)}=\frac{1}{9}\)
\(\frac{2}{90}+\frac{2}{110}+\frac{2}{132}+...+\frac{2}{x.\left(x+1\right)}=\frac{1}{9}\)
\(2\left(\frac{1}{90}+\frac{1}{110}+\frac{1}{132}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{1}{9}\)
\(2\left(\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{1}{9}\)
\(2\left(\frac{1}{9}-\frac{1}{\left(x+1\right)}\right)=\frac{1}{9}\)
\(\frac{1}{9}-\frac{1}{\left(x+1\right)}=\frac{1}{18}\)
\(\frac{1}{\left(x+1\right)}=\frac{1}{18}\)
\(x=17\)
106=45%.x + 55%.x
106=x.(45%+55%)
106.1=x.1
106=x
10^6=100%x=x
nên x=10^6