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ta có:
\(\frac{-x}{6}=\frac{-14}{9}=\frac{z}{60}=\frac{2}{-3}\)
\(\frac{-x.30}{180}=\frac{-280}{180}=\frac{z.3}{180}=\frac{-120}{180}\)
=>-x .30=-120
z.3=-120(vì -280 không chia hết cho 30 và 3)
=> x =-4
z=-40
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(\frac{2}{3}\)là phân số tối giản
nên \(\frac{-x}{6}=\frac{2}{3}\)
\(\Rightarrow\text{-x.3=2.6}\)
\(\Rightarrow-x.3=12\)
\(\Rightarrow x=-4\)
Tương tự \(\frac{14}{-y}=\frac{2}{3}\)
\(14.3=2.y\)
\(\Leftrightarrow42=2y\)
\(\Rightarrow y=21\)
Và \(\frac{z}{60}=\frac{2}{3}\)
\(\Leftrightarrow3z=2.60\)
\(\Leftrightarrow3z=120\)
\(\Rightarrow z=40\)
Vậy x=-4
y=21
z=40
chúc bạn học tốt !
\(\frac{-x}{6}=\frac{14}{-y}=\frac{z}{60}=\frac{2}{3}\)
Xét \(\frac{-x}{6}=\frac{2}{3}\)
\(\Leftrightarrow-x.3=12\Leftrightarrow-x=4\Leftrightarrow x=-4\)
Xét \(\frac{14}{-y}=\frac{2}{3}\)
\(\Leftrightarrow14.3=-y.2\Leftrightarrow42=-y.2\Leftrightarrow y=-21\)
Xét \(\frac{z}{60}=\frac{2}{3}\)
\(\Leftrightarrow z.3=120\Leftrightarrow z=40\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(\frac{-x}{6}=\frac{14}{y}=\frac{x}{60}=\frac{2}{3}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\frac{-x}{6}=\frac{2}{3}\\\frac{14}{y}=\frac{2}{3}\\\frac{z}{60}=\frac{2}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x=\frac{2\cdot6}{3}\\y=\frac{14\cdot3}{2}\\z=\frac{2\cdot60}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-4\\y=21\\z=40\end{matrix}\right.\)
Vậy: x=-4; y=21 và z=40
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{2009}{2011}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}=\frac{2009}{4022}\)(nhân mỗi vế với 1/2)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2009}{4022}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}=\frac{1}{2011}\)
\(\Rightarrow x+1=2011\Rightarrow x=2010\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2009}{2011}\)
\(\Rightarrow\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}\right)=\frac{2009}{4022}\)
\(\Rightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2009}{4022}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\)\(=\frac{2009}{4022}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\)\(=\frac{2009}{4022}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2011}\)
\(\Rightarrow x+1=2011\)
\(\Rightarrow x=2010\)