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b) \(x-y=xy=x:y\)
Vì \(x-y=xy\)
\(\Rightarrow x=xy+y\)\(\Rightarrow x=y\left(x+1\right)\)
\(\Rightarrow\frac{x}{y}=x+1\)(1)
mà \(x-y=x:y\)\(\Rightarrow x-y=x+1\)
\(\Rightarrow y=-1\)( thỏa mãn \(y\ne0\))
Thay \(y=-1\)vào (1) ta được
\(-x=x+1\)\(\Leftrightarrow2x=-1\)\(\Leftrightarrow x=\frac{-1}{2}\)
Vậy \(x=\frac{-1}{2}\)và \(y=-1\)
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52x - 1 = 52x - 3 + 125 . 24
52x - 1 - 52x - 3 = 125 . 24
52x - 1 . (1 - \(\frac{1}{25}\)) = 3 000
52x - 1 . \(\frac{24}{25}\) = 3 000
52x - 1 = 3 000 : \(\frac{24}{25}\)
52x - 1 = 3 125
52x - 1 = 55
2x - 1 = 5
2x = 5 + 1
2x = 6
x = 6 : 2
x = 3
\(5^{2x-1}=5^{2x-3}+125.24\)
\(5^{2x}:5=5^{2x}:5^3+3000\)
\(5^{2x}:5.5^3=5^{2x}+3000\)
\(5^{2x}.5^2=5^{2x}+3000\)
\(5^{2x}.5^2-5^{2x}.1=3000\)
\(5^{2x}\left(25-1\right)=3000\)
\(5^{2x}=125=5^3\)
=> 2x = 3
=> x = 3/2
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công thức: \(\dfrac{a^m}{a^n}=a^{m-n}\)
do \(5^{2x-3}\ne0\)
=> \(\dfrac{5^{2x-1}}{5^{2x-3}}=1+24\cdot\dfrac{5^3}{5^{2x-3}}\)
\(\Rightarrow5^2=1+24\cdot5^{6-2x}\)
\(\Leftrightarrow5^{6-2x}=1\)
\(\Leftrightarrow6-2x=0\) => x=3
a; \(5^{2x-1}\) = 5\(^{2x-3}\) + 125.24
5\(^{2x-1}\) - 5\(^{2x-3}\) = 125.24
5\(^{2x-3}\).(52 - 1) = 125.24
5\(^{2x-3}\).24 = 125.24
52\(x-3\) = 125.24:24
5\(^{2x-3}\) = 125
5\(^{2x-3}\) = 53
2\(x\) - 3 = 3
2\(x\) = 6
\(x\) = 6 : 2
\(x\) = 3
![](https://rs.olm.vn/images/avt/0.png?1311)
\(5^{2x-1}=5^{2x-3}+125.24\)
\(\frac{5^{2x}}{5^1}=\frac{5^{2x}}{5^3}+5^3.24\Leftrightarrow\left(QuydongMSC=5^3\right)\Rightarrow\frac{5^2.5^{2x}}{5^3}=\frac{5^{2x}+5^3.5^3.24}{5^3}\)
\(\Leftrightarrow5^2.5^{2x}-5^{2x}=5^{\left(3+3\right)}.24\Leftrightarrow5^{2x}\left(5^2-1\right)=5^6.24\)
\(\Leftrightarrow5^{2x}\left(25-1\right)=5^6.24\Rightarrow5^{2x}=5^6\Rightarrow2x=6\Rightarrow x=\frac{6}{2}=3\)
mk ko biết nhưng mk trả lời nhanh nhất nên phải k cho mình
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\(\frac{5^{2x}}{5}=\frac{5^{2x}}{5^3}+24.5^3\)
\(5^2.5^{2x}=5^{2x}+24.5^6\)
\(5^{2x}\left(5^2-1\right)=24.5^6\)
\(5^{2x}.24=24.5^6=>2x=6=>x=3\)
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nhan 2 ve cho 5^3
5^2.5^2x=5^2x+5^6.24
5^2x(5^2-1)=5^6.24
5^2x=5^6=> x=3
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52x-1-52x-3=53.23.3
52x-1-52x-1-2=125.24
52x-1-52x-1:52=125.24
52x-1-52x-1.\(\frac{1}{25}\)=125.24
52x-1.(1-\(\frac{1}{25}\))=125.24
52x-1.\(\frac{24}{25}\)=125.24
52x-1=(125.24):\(\frac{24}{25}\)
52x-1=125.25
52x-1=53.52=55
-> 2x-1=5
2x=6
x=3