Bài 3: So sánh hai số M và N biết :
M = 2^16 và N = (2 + 1)(2^2 + 1) (2^4 + 1) (2^8 + 1)
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DN
2
Những câu hỏi liên quan
5 tháng 9 2021
\(N=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1008}+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1008}+1\right)=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1008}+1\right)=2^{2016}-1< 2^{2016}=M\)
DC
1
12 tháng 11 2023
\(N=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)
=>N<M
25 tháng 9 2021
\(3,\\ a,=a^2+2a+1-a^2+2a-1-3a^2+3=-3a^2+4a+3\\ b,=\left(m^3-m+1-m^2+3\right)^2=\left(m^3-m^2-m+4\right)^2\\ 4,\\ a,\Leftrightarrow25x^2+10x+1-25x^2+9=3\\ \Leftrightarrow10x=-7\Leftrightarrow x=-\dfrac{7}{10}\\ b,\Leftrightarrow-9x^2+30x-25+9x^2+18x+9=30\\ \Leftrightarrow48x=46\Leftrightarrow x=\dfrac{23}{24}\\ c,\Leftrightarrow x^2+8x+16-x^2+1=16\\ \Leftrightarrow8x=-1\Leftrightarrow x=-\dfrac{1}{8}\)
DN
2
2 tháng 9 2021
Ta có:
\(N=\left(1+2\right)\left(2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{2008}+1\right)\)
\(\Leftrightarrow N=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{2008}+1\right)\)
\(\Leftrightarrow N=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{2008}+1\right)\)
\(\Leftrightarrow N=\left(2^8-1\right)...\left(2^{2008}+1\right)\)
\(\Leftrightarrow N=2^{4016}-1>2^{2016}=M\)
22 tháng 9 2018
a)S=1+2+2^2+2^3+...+2^9
2S=2+2^2+2^3+...+2^10
2S-S=(2+2^2+2^3+2^4+...+2^10)-(1+2+2^2+2^3+...+2^9)
S=2^10-1
S=1024-1
S=1023
Ta có:5.2^8=5.256=1280
Mà 1280>1023
=>S<5.2^8
b)Ta có:M=1+2+2^2+2^3+2^4
=>2M=2+2^2+2^3+2^4+2^5
=>2M-M=(2+2^2+2^3+2^4+2^5)-(1+2+2^2+2^3+2^4)
=>M=2^5-1
Mà N=2^5-1
=>M=N
Không biết có bị sai lỗi nào hay không,nhớ kiểm tra đó
\(N=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=2^{16}-1< 2^{16}=M\)
\(N=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\\ N=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\\ N=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\\ N=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\\ N=\left(2^8-1\right)\left(2^8+1\right)=2^{16}-1< 2^{16}=M\)