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ND
2
2T
17 tháng 8 2019
Đặt \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=2^{64}-1\)
\(\Rightarrow B=2^{64}-1-2^{64}=-1\)
N
17 tháng 8 2019
Ta có : \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)=2^{64}-1\)
Thay 264 - 1 vào B, ta được :
\(2^{64}-1-2^{64}=-1\)
PL
8 tháng 6 2018
=(2^2-1)(2^2+1)(2^4+1).......(2^32+1)-2^64
=(2^4-1^2)(2^4+1).......(2^32+1)-2^64
=(2^8-1^2)......(2^32+1)-2^64
=......
=(2^64-1^2)-2^64
=-1^2=-1
lưu ý bạn nhé dấu ...là thực hiện thương tự như trên ,bài này bạn áp dụng hằng đẳng thức 3
11 tháng 8 2015
Ta có: ( 2+1 )( 22+1 )( 24+1) .....( 232+1) - 264
Thêm ( 2-1 ) vào trước thừa số 2+1
Ta có (( 2 -1 ) ( 2+1)) (22+1) ( 24+1) .....( 232+1) - 264
= (22-1) ( 22+1) (24+1).....(232+1)-264 (sử dụng hằng đẳng thức số 3)
= (24-1) ( 24+1) .......(232+1) -264 (cứ thế rút gọn đến hết) Ta còn:
= 264 -1 -264
= -1
PL
8 tháng 6 2018
=(2^2-1)(2^2+1)(2^4+1).......(2^32+1)-2^64
=(2^4-1^2)(2^4+1).......(2^32+1)-2^64
=(2^8-1^2)......(2^32+1)-2^64
=......
=(2^64-1^2)-2^64
=-1^2=-1
lưu ý bạn nhé dấu ...là thực hiện thương tự như trên ,bài này bạn áp dụng hằng đẳng thức 3
16 tháng 8 2015
=(2^2-1)(2^2+1)(2^4+1).......(2^32+1)-2^64
=(2^4-1^2)(2^4+1).......(2^32+1)-2^64
=(2^8-1^2)......(2^32+1)-2^64
=......
=(2^64-1^2)-2^64
=-1^2=-1
lưu ý bạn nhé dấu ...là thực hiện thương tự như trên ,bài này bạn áp dụng hằng đẳng thức 3
PL
8 tháng 6 2018
=(2^2-1)(2^2+1)(2^4+1).......(2^32+1)-2^64
=(2^4-1^2)(2^4+1).......(2^32+1)-2^64
=(2^8-1^2)......(2^32+1)-2^64
=......
=(2^64-1^2)-2^64
=-1^2=-1
lưu ý bạn nhé dấu ...là thực hiện thương tự như trên ,bài này bạn áp dụng hằng đẳng thức 3
2T
3 tháng 9 2019
b) \(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^{64}-1\right)-2^{64}\)
\(=-1\)
S
3 tháng 9 2019
\(\left(1^2-2^2\right)+\left(3^2-4^2\right)+....+\left(99^2-100^2\right)\)
\(=\left(1-2\right)\left(2+1\right)+\left(3-4\right)\left(4+3\right)+....+\left(99-100\right)\left(100+99\right)\)
\(=\left(-1\right)\left(1+2+3+....+100\right)=\frac{\left(-1\right)100.99}{2}=-4950\)
31 tháng 5 2022
Bài 2:
a: \(\left(a-b-2\right)^2-\left(2a-2b\right)\left(a-b-2\right)+a^2-2ab+b^2\)
\(=\left(a-b\right)^2-4\left(a-b\right)+4+\left(a-b\right)^2-2\left(a-b\right)\left(a-b-2\right)\)
\(=2\left(a-b\right)^2-4\left(a-b\right)+4-2\left[\left(a-b\right)^2-2\left(a-b\right)\right]\)
\(=2\left(a-b\right)^2-4\left(a-b\right)+4-2\left(a-b\right)^2+4\left(a-b\right)\)
\(=4\)
b: \(\left(2+1\right)\left(2^2+1\right)\cdot...\cdot\left(2^{256}+1\right)-1\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\cdot...\cdot\left(2^{256}+1\right)-1\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\cdot...\cdot\left(2^{256}+1\right)-1\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\cdot...\cdot\left(2^{256}+1\right)-1\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\cdot...\cdot\left(2^{256}+1\right)-1\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\cdot...\cdot\left(2^{256}+1\right)-1\)
\(=\left(2^{64}-1\right)\left(2^{64}+1\right)\left(2^{128}+1\right)\left(2^{256}+1\right)-1\)
\(=\left(2^{128}-1\right)\left(2^{128}+1\right)\left(2^{256}+1\right)-1\)
\(=\left(2^{256}-1\right)\left(2^{256}+1\right)+1\)
\(=2^{512}-1+1=2^{512}\)
c: \(24\left(5^2+1\right)\left(5^4+1\right)\cdot...\cdot\left(5^{32}+1\right)-5^{64}\)
\(=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)-5^{64}\)
\(=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)-5^{64}\)
\(=\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)-5^{64}\)
\(=\left(5^{32}-1\right)\left(5^{32}+1\right)-5^{64}\)
=-1
YC
2
DN
1
T
7 tháng 10 2015
3(22+1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(22-1)(22+1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(24-1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(28-1)(28+1)(216+1)(232+1)(264+1)
=(216-1)(216+1)(232+1)(264+1)
=(232-1)(232+1)(264+1)
=(264-1)(264+1)
=(2128-1)
Nếu thấy đúng thì thích cho mình nha
PP
2
15 tháng 8 2016
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+2\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^{64}-1\right)\left(2^{64}+1\right)=2^{128}-1\)
15 tháng 8 2016
Ta có ; \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)\)
= ............................................................................................
\(=\left(2^{64}-1\right)\left(2^{64}+1\right)=2^{128}-1\)
Đặt \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(\Rightarrow\left(2-1\right)A=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(\Rightarrow A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(\Rightarrow A=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(\Rightarrow A=\left(2^8-1\right)...\left(2^{32}+1\right)-2^{64}\)
\(\Rightarrow A=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)
\(\Rightarrow A=2^{64}-1-2^{64}\)
\(\Rightarrow A=-1\)
Vậy A = -1