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a) 128-3(x+4)=23
3(x+4)=128-23
3(x+4)=105
x+4=105:3
x+4=35
x=35-4
x=31
b) [(4x+28).3+55]:5=35
(4x+28).3+55=35.5
(4x+28).3+55=175
(4x+28).3=175-55
(4x+28).3=120
4x+28=120:3
4x+28=40
4x=40+28
4x=68
x=68:4
x=17
c) ( 12x - 43 ) . 83 = 4 . 84
12x-64=4.(84:83)
12x-64=4.8
12x-64=32
12x=32+64
12x=96
x=96:12
x=8
d) 720 : [ 4 - ( 2x - 5 ) ] = 23 . 5
720:[4-(2x-5)] = 8.5
720:[4-(2x-5)]=40
4-(2x-5)=720:40
4-(2x-5)=18
2x-5=4-18
2x-5=-14
2x=-14+5
2x=-9
x=-9:2
x=\(\frac{-9}{2}\)
\(A=\frac{10^8+2}{10^8-1}\)
\(A=\frac{(10^8-1)+3}{10^8-1}\)
\(A=\frac{10^8-1}{10^8-1}+\frac{3}{10^8-1}=1+\frac{3}{10^8-1}\)
\(B=\frac{10^8}{10^8-3}=\frac{\left(10^8-3\right)+3}{10^8-3}=\frac{10^8-3}{10^8-3}+\frac{3}{10^8-3}=1+\frac{3}{10^8-3}\)
Ta thấy:
\(10^8-1>10^8-3\)
\(\Rightarrow\frac{3}{10^8-1}< \frac{3}{10^8-3}\)
\(\Rightarrow1+\frac{3}{10^8-1}< 1+\frac{3}{10^8-3}\)
\(\Rightarrow A< B\)
P/s: Hoq chắc nên đừng :((
\(A=\frac{10^8+2}{10^8-1}\)
\(A=\frac{10^8-1+3}{10^8-1}\)
\(A=1+\frac{3}{10^8-1}\)
\(B=\frac{10^8}{10^8-3}\)
\(B=\frac{10^8-3+3}{10^8-3}\)
\(B=1+\frac{3}{10^8-3}\)
\(\text{Vì }\frac{3}{10^8-1}< \frac{3}{10^8-3}\)
\(\Rightarrow1+\frac{3}{10^8-1}< 1+\frac{3}{10^8-3}\)
\(\Rightarrow A< B\)
\(A=7^3+7^4+7^5+7^6+...+7^{97}+7^{98}\)
\(=\left(7^3+7^4\right)+\left(7^5+7^6\right)+....+\left(7^{97}+7^{98}\right)\)
\(=7^3\left(1+7\right)+7^5\left(1+7\right)+...+7^{97}\left(1+7\right)\)
\(=\left(1+7\right)\left(7^3+7^5+...+7^{97}\right)\)
\(=8\left(7^3+7^5+...+7^{97}\right)⋮8\)
Vì A có: 96 số hạng nên ta chia A thành 48 nhóm 1 nhóm có 2 số hạng
\(A=7^3+7^4+7^5+7^6+...........+7^{97}+7^{98}\)
\(A=\left(7^3+7^4\right)+\left(7^5+7^6\right)+...........+\left(7^{97}+7^{98}\right)=7^3\left(1+7\right)+7^5\left(1+7\right).....+7^{97}\left(1+7^{ }\right)\)
\(A=7^3.8+7^5.8+.......+7^{97}.8=8\left(7^3+7^5+........+7^{97}\right)⋮8\left(ĐPCM\right)\)
a ) 5x-2 - 32 = 24 - ( 28 . 24 - 210 . 22 )
5x-2 - 9 = 16 - ( 256 . 16 - 1024 . 4 )
5x-2 - 9 = 16 - ( 4096 - 4096 ) = 16 - 0
5x-2 = 16 + 9 = 25 nhưng\(\sqrt{25}=5^2\)x = 2 + 2 = 4
b ) b ) 697 : [( 15 x + 364 ) : x ] = 17
mình ko hiểu đề cho lắm
4x+4x+2=272
4x+4x.42=272
4x.1+4x.16=272
4x.(16+1)=272
4x.17=272
4x=272:17
4x=16=42
=>x=2
\(x^{50}=x\)
\(=>x\in\left\{1;0\right\}\)
\(\left(2^x+1\right)^3=125\)
\(\left(2^x+1\right)^3=5^3\)
\(2^x+1=5\)
\(2^x=4\)
\(2^x=2^2\)
\(=>x=2\)
( x - 1 )3 = 84
( x - 1 )3 = ( 23 )4
( x - 1 )3 = 23.4
( x - 1 )3 = 212
( x - 1 )3 = ( 24 )3
( x - 1 )3 = 163
=> x - 1 = 16
=> x = 17
Vậy x = 17