\(\frac{144}{x-3}-\frac{144}{x}=4\)
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Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{X}{-3}=\frac{Y}{-4}=\frac{Z}{5}=>\frac{X+Y+Z}{-3+-4+5}=\frac{-144}{-2}=72\)
+ ) \(\frac{X}{-3}=72=>X=-3\cdot72=-216\)
+ ) \(\frac{Y}{-4}=72=>X=-4\cdot72=-288\)
+ )\(\frac{Z}{5}=72=>Z=5\cdot72=360\)
Vậy X = - 216
Y = - 288
Z = 360
![](https://rs.olm.vn/images/avt/0.png?1311)
a)Vì \(\frac{x}{19}=\frac{y}{21}\Rightarrow\frac{2x}{38}=\frac{y}{21}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\Leftrightarrow\frac{2x}{38}=\frac{y}{21}=\frac{2x-y}{38-21}=\frac{34}{17}=2\)
\(\Leftrightarrow\hept{\begin{cases}\frac{x}{19}=2\\\frac{y}{21}=2\end{cases}\Rightarrow\hept{\begin{cases}x=38\\y=42\end{cases}}}\)
b)Vì x + y + z =18
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\Leftrightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{x+y+z}{2+3+4}=\frac{18}{9}=2\)
\(\Rightarrow\hept{\begin{cases}\frac{x}{2}=2\\\frac{y}{3}=2\\\frac{z}{4}=2\end{cases}\Rightarrow}\hept{\begin{cases}x=4\\y=6\\z=8\end{cases}}\)
c)\(2^x+2^{x+3}=144\)
\(\Leftrightarrow2^x+2^x.2^3=144\)
\(\Leftrightarrow2^x.\left(2^3+1\right)=144\)
\(\Leftrightarrow2^x.9=144\)
\(\Leftrightarrow2^x=16=2^4\)
Vậy x=4
a) \(\frac{x}{19}=\frac{y}{21}=\frac{2x}{38}\)
Áp dụng tính chất dãy tỉ số bằng nhau. ta có:
\(\frac{x}{19}=\frac{2x}{38}=\frac{y}{21}=\frac{2x-y}{38-21}=\frac{34}{17}=2\)
Từ \(\frac{x}{19}=2\Rightarrow x=2.19=38\)
\(\frac{y}{21}=2\Rightarrow y=2.21=42\)
Vậy x = 38 ; y=42
c) \(2^x+2^{x+3}=144\)
\(\Rightarrow2^x+2^x\times2^3=144\)
\(\Rightarrow2^x.\left(1+2^3\right)=144\)
\(\Rightarrow2^x.9=144\)
\(\Rightarrow2^x=144\div9=16=2^4\)
\(\Rightarrow x=4\)
Vậy x = 4
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\(\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{9}\right)\cdot\left(1-\frac{1}{16}\right)\cdot...\cdot\left(1-\frac{1}{444}\right)\cdot\left(1-\frac{1}{169}\right)\)
\(=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{143}{144}\cdot\frac{168}{169}\)
\(=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot....\cdot\frac{11.13}{12.12}\cdot\frac{12.14}{13.13}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot11\cdot12}{2\cdot3\cdot4\cdot...\cdot12\cdot13}\cdot\frac{3\cdot4\cdot5\cdot....\cdot13\cdot14}{2\cdot3\cdot4\cdot....\cdot12\cdot13}\)
\(=\frac{1}{13}\cdot\frac{14}{2}=\frac{7}{13}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Sửa lại nha :
Ta có : \(\frac{x}{y}=\frac{3}{4}\Rightarrow\frac{x}{3}=\frac{y}{4}\left(1\right)\)
\(\frac{y}{z}=\frac{4}{5}\Rightarrow\frac{y}{4}=\frac{z}{5}\left(2\right)\)
\(\Rightarrow\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)
Áp dung tính chất của dãy tỉ số bằng nhau , ta có :
\(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}=\frac{x+y+z}{3+4+5}=\frac{144}{12}=12\)
\(\Rightarrow\begin{cases}\frac{x}{3}=12\Rightarrow x=36\\\frac{y}{4}=12\Rightarrow y=48\\\frac{z}{5}=12\Rightarrow z=60\end{cases}\)
Vậy \(\begin{cases}x=36\\y=48\\z=60\end{cases}\)
Ta có: \(\frac{x}{y}=\frac{3}{4}\Rightarrow\frac{x}{3}=\frac{y}{4}\)
\(\frac{y}{z}=\frac{4}{5}\Rightarrow\frac{y}{4}=\frac{z}{5}\)
Từ hai điều trên.Ta suy ra được:
\(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}=\frac{x+y+z}{3+4+5}=\frac{144}{12}=12\)
vậy: x = 12 . 3 = 36
y = 12 . 4 = 48
z = 12 . 5 = 60
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{3x+25}{144}=\frac{2y-169}{25}=\frac{z+144}{169}=\frac{3x+2y+z}{338}=\frac{169}{338}=\frac{1}{2}\)
\(\Rightarrow3x+25=\frac{1}{2}.144=72\)
\(\Leftrightarrow x=\frac{47}{3}\)
\(2y-169=\frac{1}{2}.25=\frac{25}{2}\)
\(\Leftrightarrow y=\frac{363}{4}\)
\(z+144=\frac{1}{2}.169=\frac{169}{2}\)
\(\Leftrightarrow z=\frac{-119}{2}\)
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
\(\frac{3x+25}{144}=\frac{1}{2}\Rightarrow6x+50=144\Rightarrow6x=94\Rightarrow x=\frac{47}{3}\)
\(\frac{2y-169}{25}=\frac{1}{2}\Rightarrow4y-338=25\Rightarrow4y=363\Rightarrow y=\frac{363}{4}\)
\(\frac{z+144}{169}=\frac{1}{2}\Rightarrow2z+288=169\Rightarrow2z=-119\Rightarrow z=\frac{-119}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\frac{144}{x+2}-\frac{100}{x}=-2\)
\(\frac{144x-100x-200}{x^2+2x}=-2\)
\(\frac{44x-200}{x^2+2x}=-2\)
\(-2x^2-4x=44x-200\)
\(-2x^2=48x-200\)
\(-2\left(x^2+24x-100\right)=0\)
\(x^2+2.12.x+144-244=0\)
\(\left(x+12\right)^2=244\)
\(\Rightarrow\hept{\begin{cases}x=\sqrt{244}-12\\x=-\sqrt{244}-12\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x-144}{10}+\frac{x-130}{12}+\frac{x-112}{14}+\frac{x-106}{16}+\frac{x-96}{17}=15\)
\(\Leftrightarrow\)\(\frac{x-144}{10}-1+\frac{x-130}{12}-2+\frac{x-112}{14}-3+\frac{x-106}{16}-4+\frac{x-96}{17}-5=0\)
\(\Leftrightarrow\)\(\frac{x-154}{10}+\frac{x-154}{12}+\frac{x-154}{14}+\frac{x-154}{16}+\frac{x-154}{17}=0\)
\(\Leftrightarrow\)\(\left(x-154\right)\left(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\right)=0\)
\(\Leftrightarrow\)\(x-154=0\) (do 1/10 + 1/12 + 1/14 + 1/16 + 1/17 khác 0)
\(\Leftrightarrow\)\(x=154\)
Vậy...
\(\frac{144}{x-3}-\frac{144}{x}=4\)
\(144x-144\left(x-3\right)=4\)
\(144x-144x+144.3=4\)
\(144x-144x+432=4\)
\(432-4\)
=> Không tìm được x thỏa mãn
nhầm 432 = 4 nhé