2mu x +1 +5nhan 2 mu x +2 =88
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Cm 1/2 mu 2 - 1/ 2mu 4 + 1/ 2 mu 6-...-1/2mu 4n -2 -1/2 mu 4n + ...+ 1/ 2 mu 2014 - 1/ 2 mu 2016<0,2
A= \(2^0+2^1+2^2+...+2^{50}\)
\(\Rightarrow\)2A =2(\(2^0+2^1+2^2+...+2^{50}\))
\(\Rightarrow\)2A= \(2+2^2+2^3+2^4+...+2^{51}\)
\(\Rightarrow\)2A-A= (\(2+2^2+2^3+2^4+...+2^{51}\))-(\(2+2^2+2^3+2^4+...+2^{50}\))
\(\Rightarrow\)A= \(2^{51}-1\)
Cm 1/2 mu 2 - 1/ 2mu 4 + 1/ 2 mu 6-...-1/2mu 4n -2 -1/2 mu 4n + ...+ 1/ 2 mu 2014 - 1/ 2 mu 2016<0,2
\(A=\frac{1}{2^2}-\frac{1}{2^4}+\frac{1}{2^6}-...+\frac{1}{2^{2014}}-\frac{1}{2^{2016}}\)
\(\Rightarrow2^2A=1-\frac{1}{2^2}+\frac{1}{2^4}-\frac{1}{2^6}+\frac{1}{2^8}-...+\frac{1}{2^{2012}}-\frac{1}{2^{2014}}\)
\(\Rightarrow2^2A+A=1+\left(\frac{1}{2^2}-\frac{1}{2^2}\right)+\left(\frac{1}{2^4}-\frac{1}{2^4}\right)+...+\left(\frac{1}{2^{2014}}-\frac{1}{2^{2014}}\right)-\frac{1}{2^{2016}}\)
\(\Rightarrow5A=1-\frac{1}{2^{2016}}< 1\Rightarrow A< \frac{1}{5}=0,2\)
\(2^{x+1}+5.2^{x+2}=88\)
\(\Rightarrow2^x.2+5.2^x.2^2=88\)
\(\Rightarrow2^x\left(2+5.2^2\right)=88\)
\(\Rightarrow2^x.22=88\)
\(\Rightarrow2^x=4\)
\(\Rightarrow2^x=2^2\)
\(\Rightarrow x=2\)
Vậy x = 2
Theo bài ra ta có:
2x+1+5.2x+2 = 88
=> 2x.2+5.2x.22
=> 2x.( 2 = 5.22 )
=> 2x.22 = 88
=> 2x = 88:22
=> 2x = 4
=> x = 4:2
=> x = 2
Vậy x = 2