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\(2A=2+2^2+2^3+2^4+2^5+...+2^{2020}\)
\(A=2A-A=2^{2020}-1\)
2(4x+35)=510
4x+35=510:2
4x+35=255
4x=255-35
4x=220
x=220:4
x=55
vậy x=55
320+(413-x)=534
413-x=534-320
413-x=214
x=413-214
x=199
vậy x=199
(x-6)2=16
* (x-6)2=42 (x-6)2=(-4)2
x-6=4 x-6=-4
x=10 x=2
vậy x=10 hoặc x=2
3(9x+2)=60
9x+2=60:3
9x+2=20
9x=18
x=18:9
x=2
vậy x=2
2(4X+35)=510
4X+35=510/2
4X+35=255
4X =255-35
4X =220
X=220/4
X=55
VẬY X =55
\(2.2^2.2^3.2^4.........2^{100}\)
\(=2^{1+2+3+4+......+100}\)
\(=2^{5050}\)
Ta co : \(\frac{\sqrt{x+1}}{\sqrt{x-3}}=\frac{\sqrt{x-3+4}}{\sqrt{x-3}}=\frac{\sqrt{x-3}}{\sqrt{x-3}}+\frac{4}{\sqrt{x-3}}\)\(=1+\frac{4}{\sqrt{x-3}}\)
De x nguyen thi \(1+\frac{4}{\sqrt{x-3}}\)nguyen
\(\Rightarrow\)\(\frac{4}{\sqrt{x-3}}\)nguyen\(\Rightarrow\)4 chia het cho \(\sqrt{x-3}\)
\(\Rightarrow\)4\(\in B\)cua \(\sqrt{x-3}\)
\(\Rightarrow\sqrt{x-3}\in\left\{4;-4;2;-2;1;-1\right\}\)
TH1 : \(\sqrt{x-3}=4\)
\(\Rightarrow x-3=16\Rightarrow x=19\)\(\Rightarrow\)chon
TH2 : \(\sqrt{x-3}=-4\) vo ly \(\Rightarrow\) loai
TH3 : \(\sqrt{x-3}=2\Rightarrow x-3=4\Rightarrow x=7\Rightarrow\)chon
TH4 : \(\sqrt{x-3}=-2\Rightarrow\)vo ly \(\Rightarrow\)chon
TH5 : \(\sqrt{x-3}=1\Rightarrow x-3=1\Rightarrow x=4\Rightarrow\)chon
TH6 : \(\sqrt{x-3}=-1\Rightarrow\)vo ly\(\Rightarrow\)loai
Vay x\(\in\){19;7;4}
B = (5 + 5^2+5^3) +...+ ( 5 ^ 2017 + 5^2018 + 5^2019)
= 5 ( 1+5+5^2)+.....+ 5^2017(1+5+5^2)
= 5. 31+....+ 5^2017 . 31
=31. ( 5+...+ 5^2017) chia hết cho 31 ( đpcm)
Vậy B chia hết cho 31