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Lê Tài Bảo Châu
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Osi
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do linh
6 tháng 5 2018 lúc 21:24

pt \(\Leftrightarrow\left(\frac{x-2}{27}-1\right)+\left(\frac{x-3}{26}-1\right)+\left(\frac{x-4}{25}-1\right)+\left(\frac{x-5}{24}-1\right)+\left(\frac{x-44}{5}+3\right)=0\)

\(\Leftrightarrow\frac{x-29}{27}+\frac{x-29}{26}+\frac{x-29}{25}+\frac{x-29}{24}+\frac{x-29}{5}=0\)

\(\Leftrightarrow\left(x-29\right)\left(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\right)=0\)

Mà \(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\ne0\)

\(\Rightarrow x-29=0\Leftrightarrow x=29\)

Kim So Huyn
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Nguyễn Thị Lan Anh
2 tháng 3 2020 lúc 18:43

\(a,⇔\frac{x-23}{24}+\frac{x-23}{25}-\frac{x-23}{26}-\frac{x-23}{27}=0\)

\(⇔(x-23)(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27})=0\)

\(⇔x-23=0\) (vì \(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}>0\))

\(⇔x=23\)

\(b,⇔\frac{x+100}{98}+\frac{x+100}{97}+\frac{x+100}{96}+\frac{x+100}{95}=0\)

\(⇔(x+100)(\frac{1}{98}+\frac{1}{97}+\frac{1}{96}+\frac{1}{95})=0\)

\(⇔x+100=0\) (vì \(\frac{1}{98}+\frac{1}{97}+\frac{1}{96}+\frac{1}{95}>0\))

\(⇔x=-100\)

\(c,⇔(\frac{x+1}{2012}+1)+(\frac{x+2}{2011}+1)=(\frac{x+3}{2010}+1)+(\frac{x+4}{2009}+1)\)

\(⇔\frac{x+2013}{2012}+\frac{x+2013}{2011}-\frac{x+2013}{2010}-\frac{x+2013}{2009}=0\)

\(⇔(x+2013)(\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009})=0\)

\(⇔x+2013=0\) (vì \(\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}<0\))

\(⇔x=-2013\)

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hoang xuan quyen
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Nguyễn Thị Ngọc Mai
5 tháng 3 2015 lúc 21:50

pạn -1 vào mỗi phân số là xong. Rùi ra x\(\frac{x-2015}{1986}\)+\(\frac{x-2015}{1988}\)\(\frac{x-2015}{1990}\)+...+\(\frac{x-2015}{x1996}\)-\(\frac{x-2015}{29}\)-\(\frac{x-2015}{27}\)-...\(\frac{x-2015}{19}\)=0

<=>(x-2015)(\(\frac{1}{1986}\)+\(\frac{1}{1988}\)+... -\(\frac{1}{19}\))=0...(mà \(\frac{1}{1986}\)+...- \(\frac{1}{19}\) khác 0)

=>x-2015=0

<=> x=2015

 

 

Thảo Nguyễn
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Nguyễn Khánh DUy
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Tiểu thư họ Nguyễn
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Dương Lam Hàng
28 tháng 7 2018 lúc 14:27

Qui đồng rồi khử mẫu, ta được:

\(4x+12.\left(27-x\right)=15x+5.\left(27-x\right)\)

\(\Leftrightarrow4x+324-12x=15x+135-5x\)

\(\Leftrightarrow4x-12x-15x+5x=135-324\)

\(\Leftrightarrow-18x=-189\Leftrightarrow x=\frac{21}{2}=10,5\)

Vậy x = 10,5

nguyen thi bao tien
28 tháng 7 2018 lúc 14:28

\(\frac{x}{15}+\frac{27-x}{5}=\frac{x}{4}+\frac{27-x}{12}\)

\(\frac{x}{15}+\frac{3\left(27-x\right)}{15}=\frac{3x}{12}+\frac{27-x}{12}\)

\(\frac{x}{15}+\frac{81-3x}{15}=\frac{3x}{12}+\frac{27-x}{12}\)

\(\frac{x+81-3x}{15}=\frac{3x+27-x}{12}\)

\(\frac{-2x+81}{15}=\frac{2x+27}{12}\)

\(12\left(-2x+81\right)=15\left(2x+27\right)\)

\(-24x+972=30x+405\)

\(972-405=30x+24x\)

\(567=54x\)

\(x=567:54\)

\(x=10,5\)

ȺßҪ•Ƙιฑǥ
28 tháng 7 2018 lúc 14:30

\(\frac{x}{15}+\frac{27-x}{5}=\frac{x}{4}+\frac{27-x}{12}\)

\(\Leftrightarrow\frac{4x}{60}+\frac{12\left(27-x\right)}{5}=\frac{15x}{60}+\frac{5\left(27-x\right)}{12}\)

\(\Leftrightarrow4x+324-12x=15x+135-5x\)

\(\Leftrightarrow4x-12x-15x+5x=135-324\)

\(\Leftrightarrow-18x=-189\)

\(x=\frac{-189}{-18}=\frac{21}{2}=10,5\)

Nguyen Minh Hieu
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alibaba nguyễn
21 tháng 5 2017 lúc 10:09

\(x+\sqrt{x+\frac{1}{2}+\sqrt{x+\frac{1}{4}}}=2\)

\(\Leftrightarrow\sqrt{x+\frac{1}{4}+2.\sqrt{x+\frac{1}{4}}.\frac{1}{2}+\frac{1}{4}}=2-x\)

\(\Leftrightarrow\sqrt{\left(\sqrt{x+\frac{1}{4}}+\frac{1}{2}\right)^2}=2-x\)

\(\Leftrightarrow\sqrt{x+\frac{1}{4}}+\frac{1}{2}=2-x\)

\(\Leftrightarrow\sqrt{x+\frac{1}{4}}=\frac{3}{2}-x\)(\(x\le\frac{3}{4}\))

 \(\Leftrightarrow x^2-4x+2=0\)

\(\Leftrightarrow\hept{\begin{cases}2-\sqrt{2}\\2+\sqrt{2}\left(l\right)\end{cases}}\) 

Cao Thị Thùy Dương
21 tháng 5 2017 lúc 9:32

mình mới học lớp 5 ko biết làm 

Nguyen Minh Hieu
21 tháng 5 2017 lúc 10:23

tks alibaba

nguyễn hồng nhung
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Bùi Anh Tuấn
22 tháng 2 2020 lúc 15:30

\(\frac{x-12}{21}+\frac{x-10}{23}=\frac{x-8}{25}+\frac{x-6}{27}\)

\(\Leftrightarrow\frac{x-12-21}{21}+\frac{x-10-23}{23}-\frac{x-8-25}{25}-\frac{x-6-27}{27}=0\)

\(\Leftrightarrow\frac{x-33}{21}+\frac{x-33}{23}-\frac{x-33}{25}-\frac{x-33}{27}=0\)

\(\Leftrightarrow\left(x-33\right)\left(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\right)=0\)

Vif \(\left(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\right)\ne0\)

\(\Rightarrow x-33=0\)

\(\Rightarrow x=33\)

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Nhật Hạ
22 tháng 2 2020 lúc 15:35

\(\frac{x-12}{21}+\frac{x-10}{23}=\frac{x-8}{25}+\frac{x-6}{27}\)

\(\Leftrightarrow\frac{x-12}{21}+1+\frac{x-10}{23}+1=\frac{x-8}{25}+1+\frac{x-6}{27}+1\)

\(\Leftrightarrow\frac{x-33}{21}+\frac{x-33}{23}=\frac{x-33}{25}+\frac{x-33}{27}\)

\(\Leftrightarrow\frac{x-33}{21}+\frac{x-33}{23}-\frac{x-33}{25}-\frac{x-33}{27}=0\)

\(\Leftrightarrow\left(x-33\right)\left(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\right)=0\)

Mà \(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\ne0\)

\(\Rightarrow x-33=0\)

\(\Leftrightarrow x=33\)

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Lê Thị Nhung
22 tháng 2 2020 lúc 15:38

\(\frac{x-12}{21}+\frac{x-10}{23}=\frac{x-8}{25}+\frac{x-6}{27}\)​​

\(\frac{x-12}{21}-1+\frac{x-10}{23}-1=\frac{x-8}{25}-1+\frac{x-6}{27}-1\)

\(\frac{x-33}{21}+\frac{x-33}{23}=\frac{x-33}{25}+\frac{x-33}{27}\)

\(\frac{x-33}{21}+\frac{x-33}{23}-\frac{x-33}{25}-\frac{x-33}{27}=0\)

\(\left(x-33\right).\left(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\right)=0\)

vì \(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\ne0\)

nên x-33=0 suy ra x=33

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