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a) 27/82 < 26/75 ( 2025/6250 < 2132\6250)
b) -49/78 > 64/ -95 ( - 3136/7410 > -4992/7410)
c) ta có: \(A=\frac{54.107-53}{53.107}=\frac{53.107+(107-53)}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)
\(B=\frac{135.269-133}{134.269+135}=\frac{134.269+\left(269-133\right)}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)
\(\Rightarrow A< B\)
d) ta có: \(A=\frac{3^{10}+1}{3^9+1}=\frac{3.\left(3^9+1\right)-2}{3^9+1}=\frac{3.\left(3^9+1\right)}{3^9+1}-\frac{2}{3^9+1}=3-\frac{2}{3^9+1}\)
\(B=\frac{3^9+1}{3^8+1}=\frac{3.\left(3^8+1\right)-2}{3^8+1}=\frac{3.\left(3^8+1\right)}{3^8+1}-\frac{2}{3^8+1}=3-\frac{2}{3^8+1}\)
mà \(\frac{2}{3^9+1}< \frac{2}{3^8+1}\Rightarrow3-\frac{2}{3^9+1}< 3-\frac{2}{3^8+1}\)
=> A < B
206 - {[38 + (135 : 9 - 3.5)5 ] : 1 + 101 }
206 - {[38 + (15 - 15)5 ]: 1 +101}
206 - {[38 + 05 ]: 1 +101}
206 - {[38 + 0 ]: 1 +101}
206 - {38: 1 + 101}
206 - {38+101}
206 - 139
67
206 - { [ 38 + ( 135 : 32 - 3.5 )5 ] : 380 + 101 }
= 206 - { [ 38 + ( 135 : 9 - 15 )5 ] : 1 + 101 }
= 206 - { [ 38 + ( 15 - 15 )5 ] + 101 }
= 206 - { [ 38 + 05 ] + 101 }
= 206 - { 38 + 101 }
= 206 - 139
= 67.
^^
135 - 3 ( x + 1 ) = 30
3 ( x + 1 ) = 105
x + 1 = 35
x = 34
\(1005^2\cdot1005^x=1005^7\)
\(1005^{2+x}=1005^7\)
=> x + 2 = 7
=> x = 5
Vậy,........
135-x=15
x=135 - 15
x=120
Vậu x = 120
4.x=75.4-4.72
4.x=4.(75-72)
4.x=4.3
=> x= 3
Vậy x = 3
5.x-3=23.32
5.x-3=8.9
5.x-3=72
5.x=72+3
5.x=75
x=75:5
x=15
Vậy x = 15
\(3^{135}+2^{135}+3^{133}+2^{134}\)
\(=\left(3^{135}+3^{133}\right)+\left(2^{135}+2^{134}\right)\)
\(=3^{133}\cdot\left(3^2+1\right)+2^{133}\cdot\left(4+1\right)\)
\(=3^{133}\cdot10+2^{133}\cdot5\)
\(=5\cdot2\cdot\left(3^{133}+2^{132}\right)\)
\(=10\cdot\left(3^{133}+2^{132}\right)\)