\(\frac{x+121}{2020}+\frac{x+144}{22}+\frac{x+169}{23}=6.\) Tìm x

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5 tháng 8

P/s đầu tiên mẫu số là 21

5 tháng 8

\(\frac{x+121}{21}+\frac{x+144}{22}+\frac{x+169}{23}=6\)

\(\left(\frac{x+121}{21}-1\right)+\left(\frac{x+144}{22}-2\right)+\left(\frac{x+169}{23}-3\right)=0\)

\(\frac{x+100}{21}+\frac{x+100}{22}+\frac{x+100}{23}=0\)

\(\left(x+100\right)\left(\frac{1}{21}+\frac{1}{22}+\frac{1}{23}\right)=0\)

\(\frac{1}{21}+\frac{1}{22}+\frac{1}{23}>0\)

Nên \(x+100=0\)

\(x=-100\)

Vậy \(x=-100\)

11 tháng 11 2018

\(\left(\frac{x}{20}+1\right)+\left(\frac{x-1}{21}+1\right)=\left(\frac{x-2}{22}+1\right)+\left(\frac{x-3}{23}+1\right)\)

\(\frac{x+20}{20}+\frac{x+20}{21}-\frac{x+20}{22}-\frac{x+20}{23}=0\)

\(\left(x+20\right).\left(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\right)=0\)

mà \(\left(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\right)\ne0\)

=> x+20=0 => x=-20

vậy x=-20

11 tháng 11 2018

\(\frac{x}{20}+\frac{x-1}{21}=\frac{x-2}{22}+\frac{x-3}{23}\)

\(1+\frac{x}{20}+1+\frac{x-1}{21}=1+\frac{x-2}{22}+1+\frac{x-3}{23}\)

\(\frac{x+20}{20}+\frac{21+x-1}{21}=\frac{22+x-2}{22}+\frac{23+x-3}{23}\)

\(\frac{x+20}{20}+\frac{x+20}{21}=\frac{x+20}{22}+\frac{x+20}{23}\)

\(\frac{x+20}{20}+\frac{x+20}{21}-\frac{x+20}{22}-\frac{x+20}{23}=0\)

\(\left(x+20\right)\left(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\right)=0\)

Mà \(\frac{1}{20}+\frac{1}{21}-\frac{1}{22}-\frac{1}{23}\ne0\)

\(\Rightarrow x+20=0\)

\(\Rightarrow x=-20\)

Vậy x = -20

10 tháng 11 2019

a) 74x.(3312+33332020+333333303030+3333333342424242)=32\frac{7}{4}x.\left(\frac{33}{12}+\frac{3333}{2020}+\frac{333333}{303030}+\frac{33333333}{42424242}\right)=3247​x.(1233​+20203333​+303030333333​+4242424233333333​)=32

74x.(3312+3320+3330+3342)=32\frac{7}{4}x.\left(\frac{33}{12}+\frac{33}{20}+\frac{33}{30}+\frac{33}{42}\right)=3247​x.(1233​+2033​+3033​+4233​)=32

74x.(333.4+334.5+335.6+336.7)=32\frac{7}{4}x.\left(\frac{33}{3.4}+\frac{33}{4.5}+\frac{33}{5.6}+\frac{33}{6.7}\right)=3247​x.(3.433​+4.533​+5.633​+6.733​)=32

74x.33.(13−14+14−15+15−16+16−17)=32\frac{7}{4}x.33.\left(\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)=3247​x.33.(31​−41​+41​−51​+51​−61​+61​−71​)=32

74x.33.(13−17)=32\frac{7}{4}x.33.\left(\frac{1}{3}-\frac{1}{7}\right)=3247​x.33.(31​−71​)=32

74x.33⋅421=32\frac{7}{4}x.33\cdot\frac{4}{21}=3247​x.33⋅214​=32

10 tháng 11 2019

b) 13+16+110+115+...+2x.(x−1)=20072009\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{2}{x.\left(x-1\right)}=\frac{2007}{2009}31​+61​+101​+151​+...+x.(x−1)2​=20092007​

26+212+220+230+...+2(x−1).x=20072009\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{\left(x-1\right).x}=\frac{2007}{2009}62​+122​+202​+302​+...+(x−1).x2​=20092007​

22.3+23.4+24.5+25.6+...+2(x−1).x=20072009\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{\left(x-1\right).x}=\frac{2007}{2009}2.32​+3.42​+4.52​+5.62​+...+(x−1).x2​=20092007​

2.(12−13+13−14+14−15+15−16+...+1x−1−1x)=200720092.\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}{x-1}-\frac{1}{x}\right)=\frac{2007}{2009}2.(21​−31​+31​−41​+41​−51​+51​−61​+...+x−11​−x1​)=20092007​

2.(12−1x)=200720092.\left(\frac{1}{2}-\frac{1}{x}\right)=\frac{2007}{2009}2.(21​−x1​)=20092007​

1−2x=200720091-\frac{2}{x}=\frac{2007}{2009}1−x2​=20092007​

2x=22009\frac{2}{x}=\frac{2}{2009}x2​=20092​

=> x = 2009

17 tháng 3 2019

\(\frac{3x+25}{144}=\frac{2y-169}{25}=\frac{z+144}{169}=\frac{3x+2y+z}{338}=\frac{169}{338}=\frac{1}{2}\)

\(\Rightarrow3x+25=\frac{1}{2}.144=72\)

\(\Leftrightarrow x=\frac{47}{3}\)

\(2y-169=\frac{1}{2}.25=\frac{25}{2}\)

\(\Leftrightarrow y=\frac{363}{4}\)

\(z+144=\frac{1}{2}.169=\frac{169}{2}\)

\(\Leftrightarrow z=\frac{-119}{2}\)

17 tháng 3 2019

Áp dụng tính chất dãy tỉ số bằng nhau

\(\frac{3x+25}{144}=\frac{2y-169}{25}=\frac{z+144}{169}=\frac{\left(3x+2y+z\right)+\left(25-169+144\right)}{144+25+169}=\frac{169+25-169+144}{144+25+169}=\)

\(\frac{1}{2}\)

Ta có

\(\frac{3x+25}{144}=\frac{1}{2}\Rightarrow6x+50=144\Rightarrow6x=94\Rightarrow x=\frac{47}{3}\)

\(\frac{2y-169}{25}=\frac{1}{2}\Rightarrow4y-338=25\Rightarrow4y=363\Rightarrow y=\frac{363}{4}\)

\(\frac{z+144}{169}=\frac{1}{2}\Rightarrow2z+288=169\Rightarrow2z=-119\Rightarrow z=\frac{-119}{2}\)

17 tháng 9 2019

Hnay đi học, cô giáo có sửa cho bạn bài đó hong dọ, do cô mình giao cái bài về nhà  y sì dãy í, mà mai nộp ròi, nhưng mình k biết làm, nếu bạn biết , chỉ mình với :((

3 tháng 7 2017

a ) Ta có : \(\frac{x+11}{10}+\frac{x+21}{20}+\frac{x+31}{30}=\frac{x+41}{40}+\frac{x+101}{5}\) 

\(\Leftrightarrow\left(\frac{x+11}{10}-1\right)+\left(\frac{x+21}{10}-1\right)+\left(\frac{x+31}{30}-1\right)=\left(\frac{x+41}{40}-1\right)+\left(\frac{x+101}{50}-2\right)\)

\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{20}+\frac{x+1}{30}=\frac{x+1}{40}+\frac{x+1}{50}\)

\(\Rightarrow\frac{x+1}{10}+\frac{x+1}{20}+\frac{x+1}{30}-\frac{x+1}{40}-\frac{x+1}{50}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}-\frac{1}{40}-\frac{1}{50}\right)=0\)

Mà \(\left(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}-\frac{1}{40}-\frac{1}{50}\right)\ne0\)

Nên x + 1 = 0

=> x = -1

3 tháng 7 2017

còn b vs c thì sao ạ

26 tháng 7 2017

ta có:

\(\frac{2x}{3}=\frac{3y}{4}=\frac{5z}{6}\)=>\(\frac{2x}{90}=\frac{3y}{120}=\frac{5z}{180}\)=>\(\frac{x}{45}=\frac{y}{40}=\frac{z}{36}\)

Áp dụng tính chất của dãy tỉ số băng nhau ta có:

\(\frac{x}{45}=\frac{y}{40}=\frac{z}{36}=\frac{x+y+z}{45+40+36}=\frac{121}{121}=1\)

=>\(\frac{x}{45}=1\)=>x=45

    \(\frac{y}{40}=1\)=>y=40

    \(\frac{z}{36}=1\)=>z=36

Vậy x=45;y=40;z=36

17 tháng 7 2018

Bác viết nhộn đề gồi :v

\(.\frac{x+4}{20}+\frac{x+3}{21}+\frac{x+2}{22}+\frac{x+1}{23}=-4\)

\(\Rightarrow\frac{x+4}{20}+1+\frac{x+3}{21}+1+\frac{x+2}{22}+1+\frac{x+1}{23}+1=0\)

\(\Rightarrow\frac{x+24}{20}+\frac{x+24}{21}+\frac{x+24}{22}+\frac{x+24}{23}=0\)

\(\Rightarrow\left(x+24\right)\left(\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+\frac{1}{23}\right)=0\)

=> x=-24

    \(\frac{x+4}{20}+\frac{x+3}{21}\frac{x+2}{22}+\frac{x+1}{23}\)\(=-4\)

\(\Rightarrow\left(\frac{x+4}{20}+1\right)+\left(\frac{x+3}{21}+1\right)+\left(\frac{x+2}{22}+1\right)\)\(+\left(\frac{x+1}{23}+1\right)=0\)

\(\Rightarrow\left(\frac{x+4}{20}+\frac{20}{20}\right)+\left(\frac{x+3}{21}+\frac{21}{21}\right)\)\(+\left(\frac{x+2}{22}+\frac{22}{22}\right)+\left(\frac{x+1}{23}+\frac{23}{23}\right)=0\)

\(\frac{\Rightarrow x+24}{20}+\frac{x+24}{21}+\frac{x+24}{22}+\frac{x+24}{23}=0\)

\(\Rightarrow\left(x+24\right)+\left(\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+\frac{1}{23}\right)=0\)

Vì \(\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+\frac{1}{23}\ne0\)

\(\Rightarrow x+24=0\)

\(\Rightarrow x=24\)

Chúc bạn học tốt ( -_- )

6 tháng 9 2020

Dài đấy :))

a) \(\left|x-1\right|-\left(-2\right)^3=9\cdot\left(-1\right)^{100}\)

\(\Leftrightarrow\left|x-1\right|-\left(-8\right)=9\cdot1\)

\(\Leftrightarrow\left|x-1\right|+8=9\)

\(\Leftrightarrow\left|x-1\right|=1\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=1\\x-1=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=0\end{cases}}\)

b) \(\frac{x-2}{-4}=\frac{-9}{x-2}\)( ĐKXĐ : \(x\ne2\))

\(\Leftrightarrow\left(x-2\right)\left(x-2\right)=-4\cdot\left(-9\right)\)

\(\Leftrightarrow\left(x-2\right)^2=36\)

\(\Leftrightarrow\left(x-2\right)^2=\left(\pm6\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=6\\x-2=-6\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=8\\x=-4\end{cases}}\left(tmđk\right)\)

c) \(\frac{x-5}{3}=\frac{-12}{5-x}\)( ĐKXĐ : \(x\ne5\))

\(\Leftrightarrow\frac{x-5}{3}=\frac{-12}{-\left(x-5\right)}\)

\(\Leftrightarrow\frac{x-5}{3}=\frac{12}{x-5}\)

\(\Leftrightarrow\left(x-5\right)\left(x-5\right)=3\cdot12\)

\(\Leftrightarrow\left(x-5\right)^2=36\)

\(\Leftrightarrow\left(x-5\right)^2=\left(\pm6\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}x-5=6\\x-5=-6\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=11\\x=-1\end{cases}}\left(tmđk\right)\)

d) \(8x-\left|4x+\frac{3}{4}\right|=x+2\)

\(\Leftrightarrow8x-x-2=\left|4x+\frac{3}{4}\right|\)

\(\Leftrightarrow7x-2=\left|4x+\frac{3}{4}\right|\)(*)

\(\left|4x+\frac{3}{4}\right|\ge0\Leftrightarrow4x+\frac{3}{4}\ge0\Leftrightarrow x\ge-\frac{3}{16}\)

Vậy ta xét hai trường hợp sau :

1. \(x\ge-\frac{3}{16}\)

(*) <=>\(7x-2=4x+\frac{3}{4}\)

\(\Leftrightarrow7x-4x=\frac{3}{4}+2\)

\(\Leftrightarrow3x=\frac{11}{4}\)

\(\Leftrightarrow x=\frac{11}{12}\)(tmđk)

2. \(x< -\frac{3}{16}\)

(*) <=> \(7x-2=-\left(4x+\frac{3}{4}\right)\)

\(\Leftrightarrow7x-2=-4x-\frac{3}{4}\)

\(\Leftrightarrow7x+4x=-\frac{3}{4}+2\)

\(\Leftrightarrow11x=\frac{5}{4}\)

\(\Leftrightarrow x=\frac{5}{44}\left(ktmđk\right)\)

Vậy x = 11/12

e) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2019}{2020}\)

\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2019}{2020}\)

\(\Leftrightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2019}{2020}\)

\(\Leftrightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{4040}\)

\(\Leftrightarrow\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{4040}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2019}{4040}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2019}{4040}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{4040}\)

\(\Leftrightarrow x+1=4040\)

\(\Leftrightarrow x=4039\)

8 tháng 9 2020

ĐKXD là gì vậy