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2/3x - 3/2x = 5/12
=> ( 2/3 - 3/2 )x = 5/12
=> -5/6x = 5/12
=> x = 5/12 : -5/6
=> x = -1/2
( x + 1/2 ) . ( 2/3 - 2x ) = 0
=> x + 1/2 = 0 hoặc 2/3 - 2x = 0
=> x = -1/2 hoặc x = 1/3
Câu 1:
\(\dfrac{128}{\left(n-3\right)^3}=2\)
\(\Leftrightarrow\left(n-3\right)^3=64\)
=>n-3=4
hay n=7
Câu 2:
\(\Leftrightarrow x^3+12=57\cdot4=228\)
\(\Leftrightarrow x^3=216\)
hay x=6
a) 80 - [130 - (12 -4)2 ]
= 80 - ( 130 - 82 )
= 80 - 116
= -36
b) 541 + (218 - b) = 735
218 - b = 194
b = 24
c) 5(x + 35) =515
x+35 = 103
x = 68
d) 96 - 3(x + 1) = 42
3(x+1) = 54
x+1 = 18
x = 17
12x - 33 = 32 . 33
12x - 33 = 243
12x = 276
x = 23
\(2^{x+2}-2^x=96\)
\(\Rightarrow2^x\cdot2^2-2^x=96\)
\(\Rightarrow2^x\left(2^2-1\right)=96\)
\(\Rightarrow2^x\left(4-1\right)=96\)
\(\Rightarrow2^x\cdot3=96\)
\(\Rightarrow2^x=96:3\)
\(\Rightarrow2^x=32\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
\(5^x+5^{x+1}=750\)
\(\Rightarrow5^x+5^x\cdot5=750\)
\(\Rightarrow5^x\left(1+5\right)=750\)
\(\Rightarrow5^x\cdot6=750\)
\(\Rightarrow5^x=750:6\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
\(2^{x+3}+2^x=144\)
\(\Rightarrow2^x\cdot2^3+2^x=144\)
\(\Rightarrow2^x\left(2^3+1\right)=144\)
\(\Rightarrow2^x\cdot9=144\)
\(\Rightarrow2^x=144:9\)
\(\Rightarrow2^x=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
a) x-12=(-28)
x=(-28)+12
x=(-16)
Vậy x=(-16)
b)20+8|x-3|=52.4
20+8|x-3|=100
8|x-3|=100-20
8|x-3|=80
|x-3|=80:8
|x-3|=10
=>x-3=10 hoặc x-3=(-10)
x=10+3 x=(-10)+3
x=13 x=(-7)
Vậy x thuộc {13;-7}
c) 96-3(x+1)=42
3(x+1)=96-42
3(x+1)54
x+1=54:3
x+1=18
x=18-1
x=17
Vậy x=17
|x-3|=7-(-2)
|x-3|=9
=>x-3=9 hoặc x-3=(-9)
x=9+3 x=(-9)+3
x=12 x=(-6)
Vậy...
e) (2x-1)3=125
(2x-1)3=53
=>2x-1=5
...
Còn lại tự lm nha
Câu g tương tự câu e
a)Đặt \(A=3-3^2+3^3-3^4+...+3^{95}-3^{96}\)
\(3A=3^2-3^3+3^4-3^5+...+3^{96}-3^{97}\)
\(3A+A=\left(3^2-3^3+3^4-3^5+...+3^{96}-3^{97}\right)+\left(3-3^2+3^3-3^4+...+3^{95}-3^{96}\right)\)
\(4A=-3^{97}+3\)
\(A=\frac{-3^{97}+3}{4}\)
b)tương tự như câu a
c)\(\left(100-1^2\right)\left(100-2^2\right)\left(100-3^2\right).....\left(100-99^2\right)\)
\(=\left(10^2-1^2\right)\left(10^2-2^2\right)\left(10^2-3^2\right)....\left(10^2-10^2\right)...\left(10^2-99^2\right)\)
\(=\left(10^2-1^2\right)\left(10^2-2^2\right)\left(10^2-3^2\right)...0...\left(10^2-99^2\right)\)
=0
a) (x^3+12):4=60+(-3)
(x^3+12).1/4=57
x^3+12=228
x^3=216
x^3=6^3
=> x=6
b) 2^x+1.3=96
2^x+1.3=2^5.3
2^x+1=2^5.3:3
2^x+1=2^5
=> x+1=5
x=4
a, 541 + ( 218 - x ) = 735
=> 218 - x = 735 - 541
=> 218 - x = 194
=> x = 218 - 194
=> x = 24
Vậy x = 24
b, 96 - 3.( x + 1 ) = 42
=> 3.( x + 1 ) = 96 - 42
=> 3.( x + 1 ) = 54
=> x + 1 = 54 : 3
=> x + 1 = 18
=> x = 18 - 1
=> x = 17
Vậy x = 17
c, ( x - 36 ) : 18 = 12
=> x - 36 = 12.18
=> x - 36 = 216
=> x = 216 + 36
=> x = 252
Vậy x = 252
d, 3x + 3x+1 + 3x+2 = 13.81
=> 3x.1 + 3x.3 + 3x.32= 13.81
=> 3x.( 1 + 3 + 32 ) = 13.81
=> 3x.( 1 + 3 + 9 ) = 13.81
=> 3x.13 = 13.81
=> 3x= 13.81:13
=> 3x= 81
=> 3x = 34
=> x = 4
Vậy x = 4
12 . (x - 1) : 3 = 43 + 23
12 . (x - 1) : 3 = 72
12 . (x - 1) = 72 . 3
12 . (x - 1) = 216
(x - 1) = 216 : 12
x - 1 = 18
x = 18 + 1
x = 19
12.(x-1):3=43+23
12.(x-1):3=64+8
12.(x-1)=72
x-1=72:12
x-1=6
x=6+1
x=7
vậy x=7
2x+2-x=96
2x.22-x=96
2x.4-x=96
2x-x=96:4
2x-x=24