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24 tháng 9 2017
a) 1,62 + 4 . 0,8 . 3,4 + 3,42 = 1,62 + 2 . 1,6 . 3,4 + 3,42
= (1,6 + 3,4 )2 = 52 = 25
b) 34 .54 - (152 + 1)(152 - 1) = 34.54 - ( 154 - 1)
= 34.54 - 34.54 + 1
= 1
c) Do x= 11 \(\Rightarrow\) 12 = x + 1
Thay 12 = x+1 vào biểu thức, ta có :
x4 - (x+1)x3 + (x+1)x2 - (x+1)x + 111
= x4 - x4 - x3 + x3 +x2 -x2 - x+ 111
= - x + 111 = -11 + 111 = 100 ( do x = 11)
Vậy ................................
_______________JK ~ Liên Quân Group ______________
TH
1
20 tháng 9 2019
\(3^8.5^8-\left(15^4-1\right).\left(15^4+1\right)=15^8-\left(15^8-1\right)=15^8-15^8+1=1\)
7 tháng 7 2023
3: =(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)
=(5^8-1)(5^8+1)(5^16+1)
=(5^16-1)(5^16+1)
=5^32-1
4:
D=(4^4-1)(4^4+1)(4^8+1)*....*(4^64+1)
=(4^8-1)(4^8+1)*...*(4^64+1)
=...
=4^128-1
5: =(5^2-1)(5^2+1)(5^4+1)*...*(5^128+1)+(5^256-1)
=(5^4-1)(5^4+1)*...*(5^128+1)+5^256-1
=5^256-1+5^256-1
=2*5^256-2
LM
Lê Minh Vũ
CTVHS
VIP
8 tháng 6 2023
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\\ =\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^{16}-1\right)\left(2^{16}+1\right)\\ =2^{32}-1 \)
2 tháng 7 2021
Ta có: \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
\(=\dfrac{\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\cdot...\cdot\left(3^{64}+1\right)}{2}\)
\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\cdot...\cdot\left(3^{64}+1\right)}{2}\)
\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\left(3^{64}+1\right)}{2}\)
\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\left(3^{64}+1\right)}{2}\)
\(=\dfrac{\left(3^{32}-1\right)\left(3^{32}+1\right)\left(3^{64}+1\right)}{2}\)
\(=\dfrac{\left(3^{64}-1\right)\left(3^{64}+1\right)}{2}\)
\(=\dfrac{3^{128}-1}{2}\)
M
1
17 tháng 6 2018
\(3^8\times5^8-\left(15^4+1\right)\left(15^4-1\right)\)
\(=15^8-\left[\left(15^4\right)^2-1\right]\)
\(=15^8-15^8+1\)
\(=1\)
PA
21 tháng 8 2016
\(S=-1^2+2^2-3^2+4^2-...+2016^2\)
\(=\left(2-1\right)\left(2+1\right)+\left(4-3\right)\left(4+3\right)+...+\left(2016-2015\right)\left(2016+2015\right)\)
\(=3+7+..+4031\)
\(=2033136\)
\(A=\left(4^2+1\right)\left(4^4+1\right)\left(4^8+1\right)\left(4^{16}+1\right)\left(4^{32}+1\right)-\frac{1}{15}\times4^{64}\)
\(15A=\left(4^2-1\right)\left(4^2+1\right)\left(4^4+1\right)\left(4^{16}+1\right)\left(4^{32}+1\right)-4^{64}\)
\(15A=\left(4^4-1\right)\left(4^4+1\right)\left(4^{16}+1\right)\left(4^{32}+1\right)-4^{64}\)
\(15A=\left(4^{16}-1\right)\left(4^{16}+1\right)\left(4^{32}+1\right)-4^{64}\)
\(15A=\left(4^{32}-1\right)\left(4^{32}+1\right)-4^{64}\left(4^{32}\right)\)
\(15A=4^{64}-1-4^{64}\)
\(A=-\frac{1}{15}\)
Các câu trả lời trên đều rất tắt nên mình sửa lại nhé :
\(3^4.5^4-\left(15^2+1\right).\left(15^2-1\right)\)
\(=3^4.5^4-\left(15^2+1\right).15^2-\left(15^2+1\right).1\)
\(=3^4.5^4-15^2.15^2+1.15^2-15^2.1+1.1\)
\(=3^4.5^4-15^{2+2}+15^2-15^2+1\)
\(=\left(3.5\right)^4-15^4+15^2-15^2+1\)
\(=15^4-15^4+15^2-15^2+1\)
\(=\left(15^4-15^4\right)+\left(15^2-15^2\right)+1\)
\(=0+0+1\)
\(=1\)
\(3^4.5^4-\left(15^2+1\right)\left(15^2-1\right)\)
\(=\left(3.5\right)^4-\left(15^4-1\right)\)
\(=15^4-15^4+1\)
\(=1\)