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Ta có: \(\dfrac{x^2}{4}=\dfrac{y^2}{9}=\dfrac{z^2}{25}=\dfrac{x^2}{2^2}=\dfrac{y^2}{3^2}=\dfrac{z^2}{5^2}\rightarrow\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
`x/2=y/3=z/5=(x-y+z)/(2-3+5)=4/4=1`
`-> x/2=y/3=z/5=1`
`-> x=2*1=2, y=3*1=3, z=5*1=5`
=>x/2=y/3=z/5 và x-y+z=4
Áp dụng tính chất của DTSBN, ta được:
x/2=y/3=z/5=(x-y+z)/(2-3+5)=4/4=1
=>x=2; y=3; z=5
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\(\dfrac{x-2}{2018}=\dfrac{x-3}{2017}=\dfrac{x-4}{2016}=\dfrac{x-5}{2015}\)
\(\dfrac{x-2}{2018}+\dfrac{x-3}{2017}=\dfrac{x-4}{2016}+\dfrac{x-5}{2015}\)
\(\left(\dfrac{x-2}{2018}-1\right)+\left(\dfrac{x-3}{2017}-1\right)=\left(\dfrac{x-4}{2016}-1\right)+\left(\dfrac{x-5}{2015}-1\right)\)
\(\dfrac{x-2020}{2018}+\dfrac{x-2020}{2017}=\dfrac{x-2020}{2016}+\dfrac{x-2020}{2015}\)
\(\dfrac{x-2020}{2018}+\dfrac{x-2020}{2017}-\dfrac{x-2020}{2016}-\dfrac{x-2020}{2015}=0\)
\(\left(x-2020\right)\left(\dfrac{1}{2018}+\dfrac{1}{2017}-\dfrac{1}{2016}-\dfrac{1}{2015}\right)=0\)
\(\dfrac{1}{2018};\dfrac{1}{2017};\dfrac{1}{2016};\dfrac{1}{2015}>0\)
Nên \(x-2020=0\)
\(x=0+2020\)
\(x=2020\)
Vậy x bằng 2020
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\(\left(\dfrac{2}{5}+\dfrac{1}{4}\right)\left(\dfrac{-x}{3}+\dfrac{1}{2}\right)+\dfrac{2}{3}=\dfrac{7}{4}\)
⇔ \(\dfrac{13}{20}\left(\dfrac{-x}{3}+\dfrac{1}{2}\right)=\dfrac{7}{4}-\dfrac{2}{3}\)
⇔ \(\dfrac{13}{20}\left(\dfrac{-x}{3}+\dfrac{1}{2}\right)=\dfrac{13}{12}\)
⇔ \(\dfrac{-x}{3}+\dfrac{1}{2}=\dfrac{13}{12}:\dfrac{13}{20}\)
⇔ \(\dfrac{-x}{3}+\dfrac{1}{2}=\dfrac{5}{3}\)
⇔ \(\dfrac{-x}{3}=\dfrac{5}{3}-\dfrac{1}{2}\)
⇔ \(\dfrac{-x}{3}=\dfrac{7}{6}\)
⇔ \(\dfrac{-2x}{6}=\dfrac{7}{6}\)
⇔ -2x = 7
⇔ \(x=-\dfrac{7}{2}\)
b) \(\left(\dfrac{3}{5}-\dfrac{x}{2}\right)\left(\dfrac{4}{5}+\dfrac{1}{2}\right)-\dfrac{4}{3}=\dfrac{3}{2}\)
⇔ \(\dfrac{13}{10}\left(\dfrac{3}{5}-\dfrac{x}{2}\right)=\dfrac{3}{2}+\dfrac{4}{3}\)
⇔ \(\dfrac{13}{10}\left(\dfrac{3}{5}-\dfrac{x}{2}\right)=\dfrac{17}{6}\)
⇔ \(\dfrac{3}{5}-\dfrac{x}{2}=\dfrac{17}{6}:\dfrac{13}{10}\)
⇔ \(\dfrac{3}{5}-\dfrac{x}{2}=\dfrac{85}{39}\)
⇔ \(\dfrac{x}{2}=\dfrac{3}{5}-\dfrac{85}{39}\)
⇔ \(\dfrac{x}{2}=\dfrac{-308}{195}\)
⇔ \(\dfrac{195x}{390}=\dfrac{-616}{390}\)
⇔ 195x = -616
⇔ \(x=\dfrac{-616}{195}\)
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`#3107`
a)
\(\dfrac{11}{12}-\left(\dfrac{2}{5}+\dfrac{3}{4}x\right)=\dfrac{2}{3}?\\ \Rightarrow\dfrac{2}{5}+\dfrac{3}{4}x=\dfrac{11}{12}-\dfrac{2}{3}\\ \Rightarrow\dfrac{2}{5}+\dfrac{3}{4}x=\dfrac{1}{4}\\ \Rightarrow\dfrac{3}{4}x=\dfrac{1}{4}-\dfrac{2}{5}\\ \Rightarrow\dfrac{3}{4}x=-\dfrac{3}{20}\\ \Rightarrow x=-\dfrac{3}{20}\div\dfrac{3}{4}\\ \Rightarrow x=-\dfrac{1}{5}\)
Vậy, \(x=-\dfrac{1}{5}\)
b)
\(\dfrac{-2}{5}+\dfrac{5}{3}\cdot\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=\dfrac{-7}{6}\\ \Rightarrow\dfrac{5}{3}\cdot\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=\dfrac{-7}{6}-\dfrac{-2}{5}\\ \Rightarrow\dfrac{5}{3}\cdot\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=-\dfrac{23}{30}\\ \Rightarrow\dfrac{3}{2}-\dfrac{4}{15}x=-\dfrac{23}{30}\div\dfrac{5}{3}\\ \Rightarrow\dfrac{3}{2}-\dfrac{4}{15}x=-\dfrac{23}{50}\\ \Rightarrow\dfrac{4}{15}x=\dfrac{3}{2}-\left(-\dfrac{23}{50}\right)\\ \Rightarrow\dfrac{4}{15}x=\dfrac{49}{25}\\ \Rightarrow x=\dfrac{147}{20}\)
Vậy, \(x=\dfrac{147}{20}\)
c)
\(\dfrac{1}{2}+\dfrac{3}{4}x=\dfrac{1}{4}\\ \Rightarrow\dfrac{3}{4}x=\dfrac{1}{4}-\dfrac{1}{2}\\ \Rightarrow\dfrac{3}{4}x=-\dfrac{1}{4}\\ \Rightarrow x=-\dfrac{1}{4}\div\dfrac{3}{4}\\ \Rightarrow x=-\dfrac{1}{3}\)
Vậy, \(x=-\dfrac{1}{3}.\)
\(#Emyeu1aithatroi...\)
(2/5 + 3/4 . x)= 11/12 -2/3
(2/5 +3/4 . x)= 1/4
3/4 . x = 1/4 - 2/5
3/4 . x = -3/20
x = -3/20 : 3/4
x = -1/5
Vậy .....
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\(a,x-\dfrac{5}{7}=\dfrac{19}{21}\\ x=\dfrac{34}{21}\\ b,\dfrac{5}{3}-\left|x-\dfrac{1}{5}\right|=\dfrac{1}{3}\\ \left|x-\dfrac{1}{5}\right|=\dfrac{4}{3}\\ TH1:x-\dfrac{1}{5}=\dfrac{4}{3}\\ x=\dfrac{23}{15}\\ TH2:x-\dfrac{1}{5}=-\dfrac{4}{3}\\ x=-\dfrac{17}{15}\\ c,x-\dfrac{2}{5}=\dfrac{1}{4}\\ x=\dfrac{13}{20}\\ d,5\sqrt{x}-30=15\\ 5\sqrt{x}=45\\ \sqrt{x}=9\\ x=9^2=81\)
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ối lắm thế :((
3.
a/ Giả sử đại lượng y tỉ lệ nghịch với đại lượng x theo hệ số tỉ lệ là k
=> y = k/x
Thay x = 8 ; y = 15 vào ct y = k/x ta có
\(\dfrac{k}{8}=15\Rightarrow k=120\)
Thay \(k=120\) vào ct \(y=\dfrac{k}{x}\) ta có
\(y=\dfrac{120}{x}\)
b/ Thay x = 6 vào ct \(y=\dfrac{120}{x}\) ta có
\(y=\dfrac{120}{6}=20\)
Thay x = - 10 vào ct \(y=\dfrac{120}{x}\) ta có
\(y=\dfrac{120}{-10}=-12\)
b/ Thay y = 2 vào ct \(y=\dfrac{120}{x}\) ta có
\(2=\dfrac{120}{x}\Rightarrow x=60\)
Thay y = - 30 vào ct \(y=\dfrac{120}{x}\) ta có
\(-30=\dfrac{120}{x}\Rightarrow x=-4\)
4/
a/ Giả sử đại lượng y tỉ lệ thuận với đại lượng x theo hệ số tỉ lệ là k
=> y = xk
Thay y = 4 ; x = 6 vào ct y = xk ta có
\(4=6k\Rightarrow k=\dfrac{2}{3}\)
Thay \(k=\dfrac{2}{3}\) vào ct y = xk ta có
\(y=\dfrac{2}{3}x\)
b/ Thay x = 9 vào ct \(y=\dfrac{2}{3}x\) ta có
\(y=\dfrac{2}{3}.9=6\)
Thay y = - 8 vào ct \(y=\dfrac{2}{3}x\) ta có
\(-8=\dfrac{2}{3}x\Rightarrow x=-12\)
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\(\dfrac{3x}{5}=\dfrac{2y}{3}\Leftrightarrow\dfrac{3x}{5}.\dfrac{1}{6}=\dfrac{2y}{3}.\dfrac{1}{6}\Leftrightarrow\dfrac{3x}{30}=\dfrac{2y}{18}\Leftrightarrow\dfrac{x}{10}=\dfrac{y}{9}\Leftrightarrow\dfrac{x^2}{100}=\dfrac{y^2}{81}\)Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x^2}{100}=\dfrac{y^2}{81}=\dfrac{x^2-y^2}{100-81}=\dfrac{38}{19}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x^2=2.100=200\\y^2=2.81=162\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\pm\sqrt{200}\\y=\pm\sqrt{162}\end{matrix}\right.\)
\(\dfrac{3}{5}x=\dfrac{2}{3}y\Rightarrow\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{5}}\) và \(x^2-y^2=38\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{5}}=\dfrac{x^2}{\dfrac{4}{6}}=\dfrac{y^2}{\dfrac{6}{10}}=\dfrac{x^2+y^2}{\dfrac{4}{6}+\dfrac{6}{10}}=\dfrac{38}{\dfrac{19}{15}}=30\)
\(\dfrac{x}{\dfrac{2}{3}}=30\Rightarrow x=30.\dfrac{2}{3}=20\)
\(\dfrac{y}{\dfrac{3}{5}}=30\Rightarrow y=30.\dfrac{3}{5}=18\)
Vậy x=20 ; y=18
x=9
x=9