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11 tháng 7 2021
a) Ta có: \(A=\dfrac{16^8-1}{\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{\left(2^{16}-1\right)\left(2^{16}+1\right)}\)
\(=\dfrac{2^{32}-1}{2^{32}-1}=1\)
b) Ta có: \(B=\dfrac{\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{9^{16}-1}\)
\(=\dfrac{\left(3^2-1\right)\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\cdot\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}\)
\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)}{2\left(3^{32}-1\right)}=\dfrac{1}{2}\)
10 tháng 10 2020
TUI ĐANG GẤP CHO TÔI HỎI BÀI NÀY LỚP 2 NHA\\\\
AN CÓ 180 CÁI KẸO.BÌNH CÓ 160. HỎI BÌNH CÓ MẤY CÁI KẸO
10 tháng 10 2020
a) Ta có: \(2.4.\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\)
\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\)
\(=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(=\left(3^{16}-1\right)\left(3^{16}+1\right)\)
\(=3^{32}-1\)
NT
2
G
9 tháng 7 2019
\(A=8\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81\)
\(A=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=\left(3^{16}-1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=3^{32}-1-81^{16}\)
NN
9 tháng 7 2019
A = 8.( 32 + 1 ).( 34 + 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 32 - 1).( 32 + 1 ).( 34 + 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 34 - 1 ).( 34 + 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 38 - 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 316 - 1 ).( 316 + 1 ) - 8116
A = ( 332 - 1 ) - 8116
A = -364
7 tháng 7 2023
1: A=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)
=(3^8-1)(3^8+1)(3^16+1)
=(3^16-1)(3^16+1)
=3^32-1
2: B=(1-3^2)(1+3^2)*...*(1+3^16)
=(1-3^4)(1+3^4)(1+3^8)(1+3^16)
=1-3^32
GH
7 tháng 7 2023
1
\(A=8\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(3^{16}-1\right)\left(3^{16}+1\right)\\ =3^{32}-1\)
\(B=\left(1-3\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(1-3^2\right)\left(1+3^2\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(1-3^4\right)\left(1+3^4\right)\left(3^8+1\right)\left(3^{16}+1\right)\\ =\left(1-3^8\right)\left(1+3^8\right)\left(3^{16}+1\right)\\ =\left(1-3^{16}\right)\left(1+3^{16}\right)=1-3^{32}\)
M
0
NH
2
HT
3 tháng 9 2017
a) A = 2016.2018 = ( 2017 - 1 ).2018 = 2017.2018 - 2018 ( 1 )
B = 20172 = 2017.2017 = 2017.( 2018 - 1) = 2017.2018 - 2017 ( 2 )
Từ (1) và (2), ta thấy: - 2018 < - 2017 => 2017.2018 - 2018 < 2017.2018 - 2017 <=> 2016.2018 < 20172
Vậy A < B
~ Phần b khi nào nghĩ ra tớ sẽ làm ngay ạ :) Còn phần này chắc chắn đúng cậu nhé ~
TN
3 tháng 9 2017
b)\(x=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2x=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2x=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2x=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2x=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2x=\left(3^{16}-1\right)\left(3^{16}+1\right)\Rightarrow x=\frac{3^{32}-1}{2}\)
Thấy \(x=\frac{3^{32-1}}{2}< 3^{32}-1=y\)
ML
3
16 tháng 6 2016
B=(3+1).(3^2+1).(3^4+1).(3^8+1).(3^16 +1).2
=>B=2.(3+1)(32+1)(34+1)(38+1).(316+1)
=(3-1)(3+1)(32+1)(34+1)(38+1).(316+1)
=(32-1)(32+1)(34+1)(38+1).(316+1)
=(34-1)(34+1)(38+1).(316+1)
=(38-1)(38+1).(316+1)
=(316-1)(316+1)
=332-1=A
Vậy A=B
16 tháng 6 2016
\(B=2.\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right).\left(3^{16}+1\right)\)
\(=\left(3-1\right).\left(3+1\right).\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)
\(=\left(3^2-1\right).\left(3^2+1\right).\left(3^4+1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)
\(=\left(3^4-1\right).\left(3^4+1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)
\(=\left(3^8-1\right).\left(3^8+1\right).\left(3^{16}+1\right)\)
\(=\left(3^{16}-1\right).\left(3^{16}+1\right)\)
\(=3^{32}-1\)
Vậy A = B = 332 - 1
T
13 tháng 9 2015
c;=(50-49)(50+49)+(48-47)(48+47)+.............+(2+1)(2-1)
=50+49+48+............+1
=(50+1)50=2550:2=1275
d;=(2^4-1)(2^4+1)(2^8+1)(2^16+1)
=(2^8-1)(2^8+1)(2^16+1)
=(2^16-1)(2^16+1)
=2^32-1
e;=(3-1)(3+1)(3^2+1)...........(3^16+1)
=(3^2-1)(3^2+1)..............(3^16+1)
=(3^16-1)(3^16+1)=3^32-1
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