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VT
2
8 tháng 8 2016
Y - 1/2 - 1/6 - 1/12 - 1/20 - 1/30 - 1/42 = 1
Đặt A= - 1/2 - 1/6 - 1/12 - 1/20 - 1/30 - 1/42
\(A=-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{42}\right)\)
\(A=-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{6.7}\right)\)
\(A=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=-\left(1-\frac{1}{7}\right)\)
\(A=-\frac{6}{7}\).Thay A vào ta có \(Y-\frac{6}{7}=1\Leftrightarrow y=\frac{13}{7}\)
4 tháng 8 2018
\(a,-12\left(x-5\right)+7\left(3-x\right)=5\)
\(-12x+60+21-7x=5\)
\(-12x-7x+81=5\)
\(-19x=5-81\)
\(-19x=-76\)
\(x=-76:\left(-19\right)\)
\(x=4\)
\(Vậyx=4\)
\(b,30\left(x+2\right)-6\left(x-5\right)-24x=100\)
\(30x+60-6x-30-24x=100\)
\(30x-6x-24x+60-30=100\)
\(0x+30=100\)
\(\Rightarrow Vôlý\)
Vậy không có giá trị nào của x thỏa mãn đề bài.
\(c,-5\left(x+\frac{1}{5}\right)-\frac{1}{2}\left(x-\frac{2}{3}\right)=\frac{3}{2}x-\frac{5}{6}\)
\(-5x-1-\frac{1}{2}x-\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)
\(-5x-\frac{1}{2}x-1-\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)
\(-\frac{11}{2}x-\frac{2}{3}=\frac{3}{2}x-\frac{5}{6}\)
\(-\frac{2}{3}+\frac{5}{6}=\frac{3}{2}x+\frac{11}{2}x\)
\(-\frac{4}{6}+\frac{5}{6}=\frac{14}{2}x\)
\(\frac{1}{6}=7x\)
\(x=\frac{1}{6}:7\)
\(x=\frac{1}{6}.\frac{1}{7}\)
\(x=\frac{1}{42}\)
\(Vậyx=\frac{1}{42}\)
\(d,-3\left(x-\frac{1}{2}\right)-5\left(x+\frac{3}{5}\right)=-x+\frac{1}{5}\)
\(-3x+\frac{3}{2}-5x-3=-x+\frac{1}{5}\)
\(-3x-5x+\frac{3}{2}-3=-x+\frac{1}{5}\)
\(-8x+\frac{3}{2}-\frac{6}{2}=-x+\frac{1}{5}\)
\(-8x-\frac{3}{2}=-x+\frac{1}{5}\)
\(-\frac{3}{2}-\frac{1}{5}=-x+8x\)
\(\frac{15}{10}-\frac{2}{10}=7x\)
\(7x=\frac{13}{10}\)
\(x=\frac{13}{10}:7\)
\(x=\frac{13}{10}.\frac{1}{7}\)
\(x=\frac{13}{70}\)
\(Vậyx=\frac{13}{70}\)
14 tháng 5 2022
b: =8,12(6+8-4)=8,12x10=81,2
a: \(A=\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+...+\dfrac{1}{10\cdot11}\)
\(=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{11}\)
=1/4-1/11=7/44
c: =>0,2a+0,4a=12
=>0,6a=12
hay a=20
CN
0
TP
2
W
1 tháng 8 2019
Bài giải
\(x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}=1\)
\(x-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\right)=1\)
Đặt :
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}\)
\(A=1-\frac{1}{8}\)
\(A=\frac{7}{8}\)
Thay \(A=\frac{7}{8}\) vào biểu thức ta được :
\(x-\frac{7}{8}=1\)
\(x=\frac{7}{8}+1\)
\(x=\frac{15}{8}\)
L
1 tháng 8 2019
Bài giải
\(x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}=1\)
\(x-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\right)=1\)
\(x-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\right)=1\)
\(x-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}\right)=1\)
\(=x-\left(1-\frac{1}{8}\right)\)
\(x-\frac{7}{8}=1\)
\(x=\frac{7}{8}+1\)
\(x=\frac{15}{8}\)
28 tháng 5 2018
\(\Leftrightarrow\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\times\frac{x}{3}=\frac{5}{21}\)
\(\Leftrightarrow\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\times\frac{x}{3}=\frac{5}{21}\)
\(\Leftrightarrow\left(\frac{1}{2}-\frac{1}{7}\right)\times\frac{x}{3}=\frac{5}{21}\)
\(\Leftrightarrow\frac{5}{14}\times\frac{x}{3}=\frac{5}{21}\)
\(\Leftrightarrow\frac{x}{3}=\frac{2}{3}\)
\(\Leftrightarrow x=2\)
T
28 tháng 5 2018
\(\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right).\frac{x}{3}=\frac{5}{21}\)
\(\Rightarrow\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right).\frac{x}{3}=\frac{5}{21}\)
\(\Rightarrow\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\right).\frac{x}{3}=\frac{5}{21}\)
\(\Rightarrow\left(\frac{1}{2}-\frac{1}{7}\right).\frac{x}{3}=\frac{5}{21}\)
\(\Rightarrow\left(\frac{7}{14}-\frac{2}{14}\right).\frac{x}{3}=\frac{5}{21}\)
\(\Rightarrow\frac{5}{14}.\frac{x}{3}=\frac{5}{21}\)
\(\Rightarrow\frac{x}{3}=\frac{5}{21}:\frac{5}{14}\)
\(\Rightarrow\frac{x}{3}=\frac{2}{3}\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
9 tháng 8 2017
\(\left(x+50\%\right):\frac{7}{8}=\frac{5}{7}\)
\(\Rightarrow\left(x+\frac{1}{2}\right)=\frac{5}{7}.\frac{7}{8}\)
\(\Rightarrow x+\frac{1}{2}=\frac{5}{8}\)
\(\Rightarrow x=\frac{5}{8}-\frac{1}{2}\)
\(\Rightarrow x=\frac{1}{8}\)
Vậy...
TP
9 tháng 8 2017
Mình làm tiếp bài của bạn " I have a crazy idea "
b) \(\frac{25-x}{3}=\frac{15}{2}\)
Áp dụng tỉ lệ thức:
\(\left(25-x\right).2=15.3\)
\(\Rightarrow25-x=\frac{15.3}{2}=\frac{45}{2}\Leftrightarrow x=25-\frac{45}{2}=\frac{5}{2}\)
c) \(x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}=1\)
\(\Rightarrow x-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=1\)
\(\Rightarrow x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)=1\)
\(\Rightarrow x-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\right)=1\)
\(\Rightarrow x-\left(\frac{1}{1}-\frac{1}{7}\right)=1\Leftrightarrow x-\frac{6}{7}=1\Leftrightarrow x=1+\frac{6}{7}=\frac{13}{7}\)
JJ
0
Lời giải:
$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{x(x+1)}=\frac{3}{8}$
$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{x(x+1)}=\frac{3}{8}$
$1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-.....+\frac{1}{6}-\frac{1}{7}+\frac{1}{x(x+1)}=\frac{3}{8}$
$1-\frac{1}{7}+\frac{1}{x(x+1)}=\frac{3}{8}$
$\frac{6}{7}+\frac{1}{x(x+1)}=\frac{3}{8}$
$\frac{1}{x(x+1)}=\frac{3}{8}-\frac{6}{7}=\frac{-27}{56}$
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