\(\dfrac{x+4}{8}+\dfrac{x+3}{9}=\dfrac{x+2}{10}+\dfrac{x+1}{11}\)

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24 tháng 9 2021

\(\dfrac{x+4}{8}+\dfrac{x+3}{9}=\dfrac{x+2}{10}+\dfrac{x+1}{11}\)

\(\Leftrightarrow\left(\dfrac{x+4}{8}+1\right)+\left(\dfrac{x+3}{9}+1\right)=\left(\dfrac{x+2}{10}+1\right)+\left(\dfrac{x+1}{11}+1\right)\)

\(\Leftrightarrow\dfrac{x+12}{8}+\dfrac{x+12}{9}-\dfrac{x+12}{10}-\dfrac{x+12}{11}=0\)

\(\Leftrightarrow\left(x+12\right)\left(\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}\right)=0\)

\(\Leftrightarrow x=-12\)( do \(\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}\ne0\))

24 tháng 9 2021

\(\dfrac{x+4}{8}+\dfrac{x+3}{9}=\dfrac{x+2}{10}+\dfrac{x+1}{11}\)

\(\dfrac{x+4}{8}+1+\dfrac{x+3}{9}+1=\dfrac{x+2}{10}+1+\dfrac{x+1}{11}+1\)

\(\dfrac{x+12}{8}+\dfrac{x+12}{9}=\dfrac{x+12}{10}+\dfrac{x+12}{11}\)

\(\dfrac{x+12}{8}+\dfrac{x+12}{9}-\dfrac{x+12}{10}-\dfrac{x+12}{11}=0\)

\(\Rightarrow\left(x+12\right).\left(\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\right)=0\)

Vì \(\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\ne0\) nên \(x+12=0\)

\(\Rightarrow x=-12\)

 

8 tháng 8 2023

\(\dfrac{x-1}{11}\) + \(\dfrac{x-2}{10}\) = \(\dfrac{x-3}{9}\) + \(\dfrac{x-4}{8}\)

\(\dfrac{x-1}{11}\) - 1 + \(\dfrac{x-2}{10}\) - 1 = \(\dfrac{x-3}{9}\) - 1 + \(\dfrac{x-4}{8}\)

\(\dfrac{x-12}{11}\) + \(\dfrac{x-12}{10}\)   = \(\dfrac{x-12}{9}\) +  \(\dfrac{x-12}{8}\)

(\(x-12\)).( \(\dfrac{1}{11}\) + \(\dfrac{1}{10}\)) = (\(x-12\)) (\(\dfrac{1}{9}\) + \(\dfrac{1}{8}\))

(\(x\) - 12).( \(\dfrac{1}{11}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{9}\) - \(\dfrac{1}{8}\)) = 0

\(x-12\)                                  = 0

\(x\)                                           = 12

 

 

24 tháng 7 2017

mn ơi giúp nhé

25 tháng 11 2018

hình như thứ tự có hơi..... Mình khó hiểu để ???

25 tháng 11 2018

biết bài nào thì giúp mình bài đó nha, 0 phải làm hết đâu

17 tháng 7 2017

bài 1) ta có : \(\dfrac{2x-y}{x+y}=\dfrac{2}{3}\Leftrightarrow2\left(x+y\right)=3\left(2x-y\right)\)

\(\Leftrightarrow2x+2y=6x-3y\Leftrightarrow4x=5y\Leftrightarrow\dfrac{x}{y}=\dfrac{5}{4}\)

vậy \(\dfrac{x}{y}=\dfrac{5}{4}\)

18 tháng 7 2017

bài 1

\(\dfrac{2x-y}{x+y}=\dfrac{2}{3}\Leftrightarrow\dfrac{2.\dfrac{x}{y}-1}{\dfrac{x}{y}+1}=\dfrac{2.\dfrac{x}{y}+2-3}{\dfrac{x}{y}+1}=2-\dfrac{3}{\dfrac{x}{y}+1}=\dfrac{2}{3}\)

\(2-\dfrac{2}{3}=\dfrac{4}{3}=\dfrac{3}{\dfrac{x}{y}+1}\)

\(\left(\dfrac{x}{y}+1\right)=\dfrac{9}{4}\Rightarrow\dfrac{x}{y}=\dfrac{9}{4}-\dfrac{4}{4}=\dfrac{5}{4}\)

16 tháng 10 2018

\(B=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+\left(\dfrac{1}{2}\right)^4+...+\left(\dfrac{1}{2}\right)^{98}+\left(\dfrac{1}{2}\right)^{99}\)

\(\Rightarrow2B=1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+\left(\dfrac{1}{2}\right)^4+...+\left(\dfrac{1}{2}\right)^{97}+\left(\dfrac{1}{2}\right)^{98}\)

\(\Rightarrow2B-B=1-\left(\dfrac{1}{2}\right)^{99}\)

\(B=1-\left(\dfrac{1}{2}\right)^{99}\)

\(2,\)

\(a,\dfrac{45^{10}.2^{10}}{75^{15}}\)

\(=\dfrac{5^{10}.9^{10}.2^{10}}{25^{15}.3^{15}}\)

\(=\dfrac{5^{10}.3^{20}.2^{10}}{5^{30}.3^{15}}\)

\(=\dfrac{5^{10}.3^{15}.\left(3^5.2^{10}\right)}{5^{10}.3^{15}.\left(5^{20}\right)}\)

\(=\dfrac{3^5.2^{10}}{5^{20}}\)

\(b,\dfrac{2^{15}.9^4}{6^3.8^3}\)

\(=\dfrac{2^{15}.3^8}{2^3.3^3.2^9}=\dfrac{2^{15}.3^8}{2^{12}.3^3}=2^3.3^5\)

\(c,\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{4^{10}.2^{10}+4^{10}}{4^4.2^4+4^4.4^7}=\dfrac{4^4.\left(4^6.2^{10}+4^6\right)}{4^4.\left(2^4+4^7\right)}\)

\(=\dfrac{4^{11}+4^6}{4^8.4^7}=\dfrac{4^6.\left(4^5+1\right)}{4^6.\left(4^2-4\right)}=\dfrac{1024+1}{16-4}=\dfrac{1025}{12}\)

\(d,\dfrac{81^{11}.3^{17}}{27^{10}.9^{15}}=\dfrac{3^{44}.3^{17}}{3^{30}.3^{30}}=\dfrac{3^{61}}{3^{60}}=3\)

\(3,\)

\(a,\left(2x+4\right)^2=\dfrac{1}{4}\)

\(\left(2x+4\right)^2=\left(\dfrac{1}{2}\right)^2=\left(\dfrac{-1}{2}\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}2x+4=\dfrac{1}{2}\\2x+4=\dfrac{-1}{2}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=\dfrac{1}{2}-4=\dfrac{-7}{2}\\2x=\dfrac{-1}{2}-4=\dfrac{-9}{2}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-7}{4}\\x=\dfrac{-9}{4}\end{matrix}\right.\)

Vậy \(x\in\left\{\dfrac{-7}{4};\dfrac{-9}{4}\right\}\)

\(b,\left(2x-3\right)^2=36\)

\(\left(2x-3\right)^2=6^2=\left(-6\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}2x-3=6\\2x-3=-6\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=6+3=9\\2x=-6+3=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=\dfrac{-3}{2}\end{matrix}\right.\)

Vậy \(x\in\left\{\dfrac{9}{2};\dfrac{-3}{2}\right\}\)

\(c,5^{x+2}=628\)

\(5^{x+2}=5^4\)

\(\Rightarrow x+2=4\)

\(\Rightarrow x=4-2=2\)

Vậy \(x=2\)

\(d,\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)

\(\Rightarrow\left(x-1\right)^{x+4}-\left(x-1\right)^{x+2}=0\)

\(\Rightarrow\left(x-1\right)^{x+2}.\left[\left(x-1\right)^2-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^{x+2}=0\\\left(x-1\right)^2-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^2=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x-1=1\\x-1=-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\\x=0\end{matrix}\right.\)

Vậy \(x\in\left\{0;1;2\right\}\)

16 tháng 10 2018

Bài 1:

B= \(\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+...+\left(\dfrac{1}{2}\right)^{99}\)

2B= \(2.[\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^{99}]\)

2B= \(1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^{98}\)

⇒2B-B= \(1-\left(\dfrac{1}{2}\right)^{99}\)

B= 1

Vậy B=1

Bài 2:

a, \(\dfrac{45^{10}.2^{10}}{75^{15}}\)= \(\dfrac{\left(3^2.5\right)^{10}.2^{10}}{\left(3.5^2\right)^{15}}=\dfrac{3^{20}.5^{10}.2^{10}}{3^{15}.5^{30}}=\dfrac{3^5.2^{10}}{5^{20}}\)

b, \(\dfrac{2^{15}.9^4}{6^3.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{2^3.3^3.2^9}=\dfrac{2^{15}.3^8}{2^{12}.3^3}=2^3.3^5\)

c,\(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{\left(2.4\right)^{10}+4^{10}}{\left(2.4\right)^4+4^{11}}=\dfrac{2^{10}.4^{10}+4^{10}}{2^4.4^4+4^{11}}=\dfrac{4^{10}.\left(2^{10}+1\right)}{4^6+4^6.4^5}=\dfrac{4^{10}.\left(2^{10}+1\right)}{4^6.\left(4^5+1\right)}=\dfrac{4^{10}.\left(2^{10}+1\right)}{4^6.\left(2^{10}+1\right)}=4^4=256\)

d, \(\dfrac{81^{11}.3^{17}}{27^{10}.9^{15}}=\dfrac{\left(3^4\right)^{11}.3^{17}}{\left(3^3\right)^{10}.\left(3^2\right)^{15}}=\dfrac{3^{44}.3^{17}}{3^{30}.3^{30}}=\dfrac{3^{61}}{3^{60}}=3\)

Bài 3:

a, \(\left(2x+4\right)^2=\dfrac{1}{4}\)

\(\left(2x+4\right)^2=\left(\dfrac{1}{2}\right)^2\)

\(2x+4=\dfrac{1}{2}\)

\(2x=\dfrac{1}{2}-4\)

\(2x=-\dfrac{7}{2}\)

\(x=-\dfrac{7}{2}:2\)

\(x=-\dfrac{7}{2}.\dfrac{1}{2}\)

\(x=-\dfrac{7}{4}\)

b, \(\left(2x-3\right)^2=36\)

\(\left(2x-3\right)^2=6^2\)

\(2x-3=6\)

\(2x=9\)

\(x=\dfrac{9}{2}\)

c, \(5^{x+2}=625\)

\(5^{x+2}=5^4\)

\(x+2=4\)

\(x=2\)

1: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^6\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{18}\)

=>4x=18

hay x=9/2

2: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^{36}\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{108}\)

=>4x=108

hay x=27

3: \(\left(\dfrac{1}{81}\right)^x=\left(\dfrac{1}{27}\right)^4\)

\(\Leftrightarrow\left(\dfrac{1}{3}\right)^{4x}=\left(\dfrac{1}{3}\right)^{12}\)

=>4x=12

hay x=3

21 tháng 11 2022

1: =>1/3:x=3/5-2/3=9/15-10/15=-1/15

=>x=-1/3:1/15=5

2: \(\Leftrightarrow x\cdot\dfrac{2}{3}-3=\dfrac{2}{5}\cdot\left(-10\right)=-4\)

=>x*2/3=-1

=>x=-3/2

3: \(\Leftrightarrow\dfrac{8}{3}:x=\dfrac{25}{12}:\dfrac{-3}{50}=\dfrac{25}{12}\cdot\dfrac{-50}{3}\)

hay x=-48/625

9: =>x=-2*3/1,5=-4

8: =>2/3:x=5/2:-3/10=5/2*(-10)/3=-50/6=-25/3

=>x=-2/3:25/3=-2/3*3/25=-2/25

14 tháng 2 2018

a) \(2\left(4x-30\right)-3\left(x+5\right)+4\left(x-10\right)=5\left(x+2\right)\)

\(\Leftrightarrow8x-60-3x+15+4x-40=5x+10\)

\(\Leftrightarrow9x-35=5x+10\)

\(\Leftrightarrow9x-5x=10+35\)

\(\Leftrightarrow4x=45\)

\(\Leftrightarrow x=\dfrac{45}{4}=11,25\)

b) \(\dfrac{11}{12}-\left(\dfrac{2}{5}+x\right)=\dfrac{2}{3}\left(6x+1\right)\)

\(\Leftrightarrow\dfrac{11}{12}-\left(\dfrac{2}{5}+x\right)=4x+\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{31}{60}+x=4x+\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{31}{60}-\dfrac{2}{3}=4x-x\)

\(\Leftrightarrow3x=\dfrac{1}{60}\)

\(\Leftrightarrow x=\dfrac{1}{180}\)

c) \(\dfrac{7}{3}-\left(2x-\dfrac{1}{3}\right)=\left(-2\dfrac{1}{6}+1\dfrac{1}{2}\right):0,25\)

\(\Leftrightarrow\dfrac{7}{3}-2x+\dfrac{1}{3}=-1\dfrac{2}{3}:\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{8}{3}-2x=\dfrac{-5}{3}.4\)

\(\Leftrightarrow\dfrac{8}{3}-2x=\dfrac{-20}{3}\)

\(\Leftrightarrow2x=\dfrac{8}{3}+\dfrac{20}{3}\)

\(\Leftrightarrow2x=\dfrac{28}{3}\)

\(\Leftrightarrow x=4\dfrac{2}{3}\)

d) \(0,75+\dfrac{5}{9}:x=5\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{3}{4}+\dfrac{5}{9}:x=\dfrac{11}{2}\)

\(\Leftrightarrow\dfrac{5}{9}:x=\dfrac{11}{2}-\dfrac{3}{4}\)

\(\Leftrightarrow\dfrac{5}{9}:x=\dfrac{19}{4}\)

\(\Leftrightarrow x=\dfrac{5}{9}:\dfrac{19}{4}\)

\(\Leftrightarrow x=\dfrac{20}{171}\)

26 tháng 8 2018

3. Từ \(\dfrac{x-2}{27}=\dfrac{3}{x-2}\Rightarrow\left(x-2\right)^2=81\)

\(\Rightarrow\left(x-2\right)^2=\left(\pm9\right)^2\\ \Rightarrow\left[{}\begin{matrix}x-2=-9\\x-2=9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-7\\x=11\end{matrix}\right.\)

Vậy x = -7 hoặc x = 11

4. Từ \(\dfrac{2x+5}{9-2x}=\dfrac{2}{5}\)

\(\Rightarrow5\left(2x+5\right)=2\left(9-2x\right)\\ \Leftrightarrow10x+25=18-4x\\ \Leftrightarrow14x=-7\\ \Rightarrow x=-\dfrac{1}{2}\)

5. Từ \(\dfrac{x-7}{x+8}=\dfrac{x-8}{x+9}\)

\(\Rightarrow\left(x-7\right)\left(x+9\right)=\left(x-8\right)\left(x+8\right)\\ \Leftrightarrow x^2+2x-63=x^2-64\\ \Leftrightarrow2x=-1\\ \Rightarrow x=-\dfrac{1}{2}\)