Rút gọn biểu thức :
A= (38+1).(34+1).(32+1)(3+1)
B= 12.(52+1).(54+1).(58+1)...(532+1)
K
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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)
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: \(C=48\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^2-1\right)\left(5^2+1\right)\cdot\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{16}-1\right)\cdot\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{32}-1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{64}-1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{128}-1\right)\)
\(=2\cdot5^{128}-2\)
HH
1
NA
Ngoc Anh Thai
Giáo viên
15 tháng 5 2021
\(\left(3-1\right)A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\\ 2A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\\ 2A=\left(3^4-1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\\ 2A=\left(3^8-1\right)\left(3^8+1\right)...\left(3^{64}-1\right)\\ ...\\ 2A=\left(3^{64}-1\right)\left(3^{64}+1\right)\\ 2A=3^{128}-1\)
Vậy \(A=\dfrac{3^{128}-1}{2}.\)
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 \(n\in\left\{0;-\dfrac{2}{3};\dfrac{1}{3};-1;1;-\dfrac{5}{3}\right\}\)
AH
Akai Haruma
Giáo viên
26 tháng 8 2023
Lời giải:
a.
$=2\sqrt{5}-9\sqrt{5}-2\sqrt{5}=(2-9-2)\sqrt{5}=-9\sqrt{5}$
b.
$=36\sqrt{6}-2\sqrt{6}+6\sqrt{6}=(36-2+6)\sqrt{6}=40\sqrt{6}$
Giải:
a) \(A=\left(3^8+1\right)\left(3^4+1\right)\left(3^2+1\right)\left(3+1\right)\)
\(\Leftrightarrow2A=2\left(3^8+1\right)\left(3^4+1\right)\left(3^2+1\right)\left(3+1\right)\)
\(\Leftrightarrow2A=\left(3^8+1\right)\left(3^4+1\right)\left(3^2+1\right)\left(3+1\right)\left(3-1\right)\)
\(\Leftrightarrow2A=\left(3^8+1\right)\left(3^4+1\right)\left(3^2+1\right)\left(3^2-1\right)\)
\(\Leftrightarrow2A=\left(3^8+1\right)\left(3^4+1\right)\left(3^4-1\right)\)
\(\Leftrightarrow2A=\left(3^8+1\right)\left(3^8-1\right)\)
\(\Leftrightarrow2A=3^{16}-1\)
\(\Leftrightarrow A=\dfrac{3^{16}-1}{2}\)
Vậy ...
b) \(B=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)...\left(5^{32}+1\right)\)
\(\Leftrightarrow2B=2.12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)...\left(5^{32}+1\right)\)
\(\Leftrightarrow2B=24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)...\left(5^{32}+1\right)\)
\(\Leftrightarrow2B=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)...\left(5^{32}+1\right)\)
\(\Leftrightarrow2B=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)...\left(5^{32}+1\right)\)
...
\(\Leftrightarrow2B=\left(5^{32}-1\right)\left(5^{32}+1\right)\)
\(\Leftrightarrow2B=5^{64}-1\)
\(\Leftrightarrow B=\dfrac{5^{64}-1}{2}\)
Vậy ...