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a) pt <=> \(\frac{x\left(x+1\right)}{2}=500500\)
<=> \(x^2+x=1001000\)
<=> \(x^2-1000x+1001x-1001000=0\)
<=> \(\left(x-1000\right)\left(x+1001\right)=0\)
<=> \(\orbr{\begin{cases}x=1000\\x=-1001\end{cases}}\)
Do \(x>0\)=> \(x=1000\)
b)
<=> \(2x=210\)
<=> \(x=105\)
c)
<=> \(6x-81=3.7\)
<=> \(x=17\)
d)
<=> \(125-5\left(3x-1\right)=5^2\)
<=> \(5\left(3x-1\right)=100\)
<=> \(3x-1=20\)
<=> \(x=7\)
e)
<=> \(4^{x+1}+1=65\)
<=> \(4^{x+1}=64\)
<=> \(x+1=3\)
<=> \(x=2\)
j)
<=> \(2\left(2x-3\right)=14\)
<=> \(2x-3=7\)
<=> \(x=5\)
b) 123 - 5.(x+4) = 38
=> 5.(x+4) = 123 - 38
=> 5.(x+4) = 85
=> (x+4) = 85 : 5
=> x+4 = 17
=> x = 17 - 4
=> x = 13
c) 2.x - 138 = 23.32
=>2.x - 138 = 736
=>2.x = 736 + 138
=>2.x = 874
=> x = 874 : 2
=> x = 437
d) 70 - 5.(x-3) = 45
=> 5.(x-3) = 70 - 45
=> 5.(x-3) = 25
=> (x-3) = 25 : 5
=> x-3 = 5
=> x = 5 + 3
=> x = 8
123-5.(x+4)=38
5(x+4)=123-38
5(x+4)=85
x+4=85:5
x+4=17
x=17-4
x=13
10+2x=2.(32-1)
10+2x=2.(9-1)
10+2x=2.8
2x=16-10
2x=6
x=6:2
x=3
2.x-138=23.32
2.x-138=72
2.x=72+138
2.x=210
x=210:2
x=105
[102+(28-2x)]:20-5=1
(102+28-2x):20=6
130-2x=120
2x=130-120
2x=10
x=10:2
x=5
231-(x-6)=1339:13
231-(x-6)=103
x-6=231-103
x-6=128
x=128+6
x=134
123-5.(x+4)=38
5.(x+4)=123-38
5.(x+4)=85
(x+4)=85/5
x+4=17
x=17-4
x=13
a) \(\text{2(x-51)=2.2^2+20}\)
\(2\left(x-51\right)=2.4+20\)
\(2\left(x-51\right)=28\)
\(x-51=28\div2\)
\(x-51=14\)
\(x=14+51\)
\(\text{b)3.(x+1)-26=541}\)
\(3.\left(x+1\right)=541+26\)
\(3\cdot\left(x+1\right)=567\)
\(x+1=567\div3\)
\(x+1=189\)
\(x=189-1\)
\(x=188\)
\(x=65\)
\(\text{c)4(x-3)=7^2-1^10}\)
\(4\left(x-3\right)=49-1\)
\(4\left(x-3\right)=48\)
\(x-3=48\div4\)
\(x-3=12\)
\(x=12+3\)
\(x=15\)
\(\text{e)2x-138=2^3.3^2}\)
\(2x-138=8\cdot9\)
\(2x-138=72\)
\(2x=72+138\)
\(2x=210\)
\(x=210\div2\)
\(x=105\)
\(\text{f)(x-1)^4=16}\)
\(\left(x-1\right)^4=2^4\)
\(x-1=2\)
\(x=2+1\)
\(x=3\)
a, 123 - 5 ( x + 4 ) = 38
=> 5(x+4)=123-38
=> 5(x+4)=85
=> x+4=85:5
=>x+4=17
=>x=17-4
=>x=13
b, ( 3x - 24 ) . 73 = 2 . 74
=> (3x-16).343=4802
=> 3x-16=4802:343
=>3x-16=14
=>3x=14+16
=>3x=30
=>x=30:3
=>x=10
c, 5x+3 - 13 = 112
=> 5x+3=112+13
=>5x+3=125
=> 5x+3=53
=> x+3=3
=>x=3-3
=>x=0
a)
2x - 138 = 23 . 32
2x - 138 = 8 . 9
2x - 138 = 72
2x = 72 + 138
2x = 110
x = 110 : 2
x = 55
còn lại tương tự
1.
a) ( 57 + 59 ) . ( 68 + 610 ) . ( 24 - 42 )
= ( 57 + 59 ) . ( 68 + 610 ) . 0
= 0
b) 9 < 3x < 27
32 < 3x < 33
2 < x < 3
Vậy 2 < x < 3
2.
a) xy - 2x = 0
x ( y - 2 ) = 0
\(\Rightarrow\orbr{\begin{cases}x=0\\y-2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\y=2\end{cases}}}\)
b) ( x- 4 ) . ( x - 3 ) = 0
\(\Rightarrow\orbr{\begin{cases}x-4=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=3\end{cases}}\)
c) Ta có : 3n+2 + 3n = 3n . 32 + 3n = 3n . ( 32 + 1 ) = 3n . 10 \(⋮\)10
a) 123 - 5 (x + 4) = 38
5 (x + 4) = 123 - 38
5 (x + 4) = 85
x + 4 = 85 : 5
x + 4 = 17
x = 17 - 4
x = 13
b) (3x - 24) . 73 = 2 . 74
3x - 24 = 2 . 74 : 73
3x - 24 = 2 . 7
3x - 16 = 14
3x = 14 + 16
3x = 30
x = 30 : 3
x = 10
c) (x : 3 - 4) . 5 = 15
x : 3 - 4 = 15 : 5
x : 3 - 4 = 3
x : 3 = 3 + 4
x : 3 = 7
x = 7 . 3
x = 21
a: =>4(x-3)=49-1=48
=>x-3=12
=>x=15
b: =>123-5(x+4)=38
=>5(x+4)=123-38=85
=>x+4=17
=>x=13
c: =>2x-138=9*8=72
=>2x=72+138=210
=>x=105