Rút gọn: 12(52+1).(54+1).(58+1).(516+1)
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PT
1
CM
8 tháng 11 2018
Ta có:
( 5 2 - 1).P = ( 5 2 – 1).12.( 5 2 + 1)( 5 4 + 1)( 5 8 + 1)( 5 16 + 1)
= 12.( 5 2 – 1).( 5 2 + 1)( 5 4 + 1)( 5 8 + 1)( 5 16 + 1)
= 12.( 5 4 - 1)( 5 4 + 1)( 5 8 + 1)( 5 16 + 1)
= 12.( 5 8 - 1)( 5 8 + 1)( 5 16 + 1)
= 12.( 5 16 - 1)( 5 16 + 1)
= 12.( 5 32 - 1)
28 tháng 12 2017
Ta có: \(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(\Rightarrow P=\dfrac{24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(\Rightarrow P=\dfrac{\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(\Rightarrow P=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(\Rightarrow P=\dfrac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(\Rightarrow P=\dfrac{\left(5^{16}-1\right)\left(5^{16}+1\right)}{2}\)
\(\Rightarrow P=\dfrac{5^{32}-1}{2}\)
31 tháng 8 2021
\(C=48\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)=2\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)=2\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\left(5^{128}-1\right)=2.5^{128}-2\)
31 tháng 8 2021
c: Ta có: \(C=48\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^2-1\right)\left(5^2+1\right)\cdot\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{16}-1\right)\cdot\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{32}-1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{64}-1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{128}-1\right)\)
\(=2\cdot5^{128}-2\)
20 tháng 10 2022
Bài4:
=>x(x^2+1)=0
>x=0
Bài 5:
=>\(3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)
=>\(3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(n\in\left\{0;-\dfrac{2}{3};\dfrac{1}{3};-1;1;-\dfrac{5}{3}\right\}\)
MD
1
22 tháng 11 2015
tử số =18.123+9.4567.2+3.5310.6=18.123+18.4567+18.5310
=18(123+4567+5310)
=18.10000=180000
mẫu số = 1+4+7+....+49+52+55+58-490
=(1+58)+(4+55)+.....(28+31)-490
=59+59+59+...+59-490(10 so 59)
=100
suy ra A=180000:100=1800
25 tháng 10 2022
Bài 4:
x^3+x=0
=>x(x^2+1)=0
=>x=0
Bài 5:
\(3n^3+10n^2-5⋮3n+1\)
\(\Leftrightarrow3n^3+n^2+9n^2-1-4⋮3n+1\)
=>\(3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(n\in\left\{0;-\dfrac{2}{3};\dfrac{1}{3};-1;1;-\dfrac{5}{3}\right\}\)
17 tháng 6 2018
gọi tử là B
vậy B = 18 x 123 + 9 x 4567 x 2 + 3 x 5310 x 6
=> B = 18 x 123 + 18 x 4567 + 18 x 5310
=> B = 18 x ( 123 + 4567 + 5310 )
=> B = 18 x 10000
=> B = 180000
gọi mẫu là C
vậy C = 1 + 4 + 7 + 10 + .....+ 49 + 52 + 58 - 490
gọi 1 + 4 + 7 + 10 + .....+ 49 + 52 là D
vậy số số hạng của D là : ( 52 - 1 ) : 3 + 1 = 18
D = ( 18 x 53 ) : 2 = 477
C = 477 + 58 - 490 = 45
A = \(\frac{180000}{45}\)
A = 4000
Theo đầu bài ta có:
\(12\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)\)
\(=\frac{24}{2}\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)\)
\(=\frac{\left(5^2-1\right)\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^4-1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^8-1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^{16}-1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{5^{32}-1}{2}\)