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a)
\(2^x\left(1+2+2^2+2^3\right)=480\)
\(2^x.15=480\Rightarrow2^x=\frac{480}{15}=32=2^5\Rightarrow x=5\)
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1 (3y - 0,8 ) : y + 14,5 = 15
( 3y - 0,8 ) : y = 0,5
3y : y - 0,8 : y = 0,5
3 - 0,8 : y = 0,5
0,8 : y = 2,5
y = 0,8 : 2,5
y = 0,32
Ta có :
Tử số = 2012 x 14 + 1997 + 2010 x 2011
= ( 2011 + 1 ) x 14 + 1997 + 2010 x 2011
= 2011 x 14 + 1 x 14 + 1997 + 2010 x 2011
= 2011 x 14 + 14 + 1997 + 2010 x 2011
= ( 2011 x 14 ) + ( 14 + 1997 ) + ( 2010 x 2011 )
= 2011 x 14 + 2011 + 2010 x 2011
= 2011 x ( 14 + 1 + 2010 )
= 2011 x 2025
Mẫu số = 2011 x 5 + 2011 x 1008 + 1012 x 2011
= 2011 x ( 5 + 1008 + 1012 )
= 2011 x 2025
=> \(A=\frac{2011\times2025}{2011\times2025}=1\)
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Câu 1 bị sai đề bài.
Câu 2:
\(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}=\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}\)
\(=1-\frac{1}{2012}+1-\frac{1}{2013}+1+\frac{1}{2011}+\frac{1}{2011}\)
Vì:
\(\frac{1}{2011}>\frac{1}{2012};\frac{1}{2011}>\frac{1}{2013}\Rightarrow\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2012}-\frac{1}{2013}>0\)
\(\Rightarrow\)\(\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}>3\)
\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}>3\)
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2012.(2011-x)+25=55:53
=>2012.(2011-x)+25=55-3
=>2012.(2011-x)+25=52
=>2012.(2011-x)+25=25
=>2012.(2011-x)=25-25
=>2012.(2011-x)=0
=>2011-x=0:2012
=>2011-x=0
=>x=2011-0
=>x=2011
a) \(5^{x-3}=125\)
\(\Rightarrow5^{x-3}=5^3\)
\(\Rightarrow x-3=3\)
\(\Rightarrow x=3+3\)
\(\Rightarrow x=6\)
b) \(x^{2012}:3=3^{2011}\)
\(\Rightarrow x^{2012}=3^{2011}\cdot3\)
\(\Rightarrow x^{2012}=3^{2011+1}\)
\(\Rightarrow x^{2012}=3^{2012}\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)