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MV
6 tháng 8 2017
\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\\ \dfrac{2}{42}+\dfrac{2}{56}+\dfrac{2}{72}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\\ 2\cdot\left[\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+...+\dfrac{1}{x\left(x+1\right)}\right]=\dfrac{2}{9}\\ \dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{2}{9}:2\\ \dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{9}\\ \dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{4}{9}\\ \dfrac{1}{x+1}=\dfrac{1}{6}-\dfrac{1}{9}\\ \dfrac{1}{x+1}=\dfrac{1}{18}\\ x+1=18\\ x=17\)
Vậy x = 17
6 tháng 7 2017
a, sai đề
b, \(\dfrac{1}{21}+\dfrac{1}{28}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
\(\Rightarrow\dfrac{1}{42}+\dfrac{1}{56}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{1}{9}\) ( nhân cả 2 vế với \(\dfrac{1}{2}\) )
\(\Rightarrow\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{1}{9}\)
\(\Rightarrow\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{9}\)
\(\Rightarrow\dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{1}{9}\)
\(\Rightarrow\dfrac{1}{x+1}=\dfrac{1}{18}\Rightarrow x+1=18\Rightarrow x=17\)
Vậy x = 17
LG
6 tháng 7 2017
Câu a thiếu đề rồi bạn ơi mik giải câu b đây:
\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
\(\dfrac{2}{42}+\dfrac{2}{56}+\dfrac{2}{72}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
\(\dfrac{2}{6.7}+\dfrac{2}{7.8}+\dfrac{2}{8.9}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
\(2\left(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+....+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2}{9}\)
\(2\left(\dfrac{1}{6}-\dfrac{1}{x+2}\right)=\dfrac{2}{9}\)
\(\dfrac{1}{6}-\dfrac{1}{x+2}=\dfrac{2}{9}:2\)
\(\dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{1}{9}\)
\(\dfrac{1}{x+1}=\dfrac{1}{6}-\dfrac{1}{9}\)
\(\dfrac{1}{x+1}=\dfrac{1}{18}\)
\(\Rightarrow x+1=18\Rightarrow x=17\)
Vậy x = 17
NN
1
17 tháng 3 2017
\(\left(x:\dfrac{x}{7}+1\right):\left(-4\right)=\dfrac{-1}{28}\)
\(x:\dfrac{x}{7}+1=\dfrac{-1}{28}.\left(-4\right)\)
\(x:\dfrac{x}{7}+1=\dfrac{1}{7}\)
\(x:\dfrac{x}{7}=\dfrac{1}{7}-1\)
\(x:\dfrac{x}{7}=\dfrac{-6}{7}\)
\(x=\dfrac{-6}{7}.\dfrac{x}{7}\)
\(x=\dfrac{-6.x}{49}\)
\(x=49:\left(-6\right)\)
\(x=-\dfrac{49}{6}\)
5 tháng 8 2018
a, (x + 1) + (x + 4) + ... + (x + 28) = 155
x + 1 + x + 4 + ... + x + 28 = 155
(x + x + x + ... + x) + (1 + 4 + ... + 28) = 155
x . 10 + 145 = 155
x . 10 = 155 - 145
x . 10 = 10
x = 10 : 10
x = 1
PN
15 tháng 7 2017
1) \(\left(-1\dfrac{1}{5}+x\right):\left(-3\dfrac{3}{5}\right)=\dfrac{-7}{4}+\dfrac{1}{4}:\dfrac{1}{8}\)
\(\Leftrightarrow\left(-1\dfrac{1}{5}+x\right):\left(-3\dfrac{3}{5}\right)=\dfrac{-7}{4}+2\)
\(\Leftrightarrow\left(-1\dfrac{1}{5}+x\right):\left(-3\dfrac{3}{5}\right)=\dfrac{1}{4}\)
\(\Leftrightarrow-1\dfrac{1}{5}+x=\dfrac{1}{4}.\left(-3\dfrac{3}{5}\right)\)
\(\Leftrightarrow-1\dfrac{1}{5}+x=\dfrac{1}{4}.\left(-\dfrac{18}{5}\right)\)
\(\Leftrightarrow-1\dfrac{1}{5}+x=-\dfrac{9}{10}\)
\(\Leftrightarrow x=\left(-\dfrac{9}{10}\right)-\left(-1\dfrac{1}{5}\right)\)
\(\Leftrightarrow x=\dfrac{3}{10}\)
22 tháng 8 2017
\(y+30\%y=-1,3\\ 130\%y=-1,3\\ \Rightarrow y=\dfrac{-1,3}{130\%}=-1\)
22 tháng 8 2017
\(x:\dfrac{4}{28}=\dfrac{13}{-19}+\dfrac{8}{25}\\ 7x=-\dfrac{173}{475}\\ x=-\dfrac{\dfrac{173}{475}}{7}=-\dfrac{173}{3325}\)
6 tháng 5 2018
Câu 1:
\(\left(x-3\right)^2=16\)
\(\Rightarrow\)\(\left[{}\begin{matrix}x-3=4\\x-3=-4\end{matrix}\right.\)
\(\Rightarrow\)\(\left[{}\begin{matrix}x=7\\x=-1\end{matrix}\right.\)
vậy x\(\in\)\(\left\{7;-1\right\}\)
câu2:a,
\(\Rightarrow\)\(\dfrac{13}{30}\le x< \dfrac{77}{10}\)
mà x\(\in\)Z\(\Rightarrow\)x\(\in\)\(\left\{1;2;3;4;5;6\right\}\)
vậy x\(\in\)\(\left\{1;2;3;4;5;6\right\}\)
b, ta có: \(\dfrac{-12}{21}=\dfrac{-48}{84}\);\(\dfrac{10}{-28}=\dfrac{-10}{28}=\dfrac{-30}{84}\)
mà \(\dfrac{-48}{84}< \dfrac{-30}{84}\)\(\Rightarrow\)\(\dfrac{-12}{21}< \dfrac{10}{-28}\)
NT
6 tháng 5 2018
bạn ko nhất thiết phải làm dài dòng ở phần so sánh như thế mình có cách làm ngắn gọn hơn
-12/21<-12/-28
Mà -12/-28<10/-28
=> -12/21<10/-28
Ta có:\(\dfrac{x-1}{79}=\dfrac{-28}{1-x}\)
\(\Rightarrow\left(x-1\right)\left(1-x\right)=-28.79\)
\(\Rightarrow\left(x-1\right).1-\left(x-1\right)x=-2212\)
\(\Rightarrow x-1-x^2+x=-2212\)
\(\Rightarrow x+x-x^2=-2211\)
\(\Rightarrow2x-x^2=-2211\)
\(\Rightarrow x\left(2-x\right)=-2211\)
...
\(\dfrac{x-1}{79}=\dfrac{-28}{1-x}\)
\(\Leftrightarrow\left(x-1\right)\left(1-x\right)=\left(-28\right).79\)
\(\Leftrightarrow x\left(1-x\right)-1\left(1-x\right)=-2212\)
\(\Leftrightarrow x-x^2-1-x=-2212\)
\(\Leftrightarrow-x^2-1=-2212\)
\(\Leftrightarrow-x^2=-2211\)
\(\Leftrightarrow x^2=2211\)
\(\Leftrightarrow x=\sqrt{2211}\)