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4(x - 5) - 23 = 24.3
=> 4(x - 5) - 8 = 16.3
=> 4(x - 5) - 8 = 48
=> 4(x - 5) = 48 + 8
=> 4(x - 5) = 56
=> x - 5 = 56 : 4
=> x - 5 = 14
=> x = 14 + 5
=> x = 19
Vậy x = 19
b)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x.\left(x+1\right)}=\frac{2007}{2009}\)
\(=\frac{1}{1.3}+\frac{1}{2.3}+\frac{1}{2.5}+...+\frac{2}{x.\left(x+1\right)}=\frac{2007}{2009}\)
\(=\frac{1}{2}.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{2007}{2009}\)
\(=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2007}{2009}:\frac{1}{2}\)
\(=\frac{1}{2}-\frac{1}{x+1}=\frac{2007}{4018}\)
\(=\frac{1}{x-1}=\frac{1}{2009}\Leftrightarrow x+1=2009\)
\(\Rightarrow x=2009-1=2008\)
Bạn Phúc Trần Tấn bạn có biết làm phần a ko?Giúp mk với ạ!Mai mk cần rùi
\(x^3=x\)
\(\Rightarrow x^3-x=0\)
\(\Rightarrow x.\left(x^2-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
vậy ...
mấy câu khác tương tự
5.\(\left(x-5\right)^6=\left(x-5\right)^4\)
\(\Rightarrow\left(x-5\right)^6-\left(x-5\right)^4=0\)
\(\Rightarrow\left(x-5\right)^4.\left[\left(x-5\right)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\\left(x-5\right)^2=1\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=6\end{cases}}}\)
vậy.....
câu 6 tương tự câu 5
\(5.\left(x-5\right)^6=\left(x-5\right)^4\)
\(\Rightarrow\left(x-5\right)^6-\left(x-5\right)^4=0\)
\(\Rightarrow\left(x-5\right)^4.\left[\left(x-5\right)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\\left(x-5\right)^2+1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
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)
<=> \(2\left(2x-3\right)=14\)
<=> \(2x-3=7\)
<=> \(x=5\)
a) A = 5 + 52 + 53 + .... + 5100
=> 5A = 52 + 53 + .... + 5101
=> 5A - A = (52 + 53 + .... + 5101) - (5 + 52 + 53 + .... + 5100)
=> 4A = 5101 - 5
=> A = \(\frac{5^{101}-5}{4}=\frac{5\left(5^{100}-1\right)}{4}\)
8 ≤ |x - 6|< 9
|x - 6| = 8
x - 6 = 8 hoặc x - 6 = -8
x = 8 + 6 hoặc x = -8 + 6
x = 14 hoặc x = -2
(42 + 32) . x + (42 - 32) . x - 5x = 34
(16 + 9) . x + (16 - 9) . x - 5x = 81
(16 + 9) . x + (16 - 9) . x - 5x = 81
25x + 7x - 5x = 81
(25 + 7 - 5)x = 81
27x = 81
x = 81 : 27
x = 3
a)120-3(x+4)=23
=>3(x+4)=120-23
=>3(x+4)=97
=>x+4=97:3
=>x+4=\(\frac{97}{3}\)
=>x=\(\frac{97}{3}\)-4
=>x=\(\frac{85}{3}\)
Vậy x=\(\frac{85}{3}\)
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=12
=>x=12:4
=>x=3
Vậyx= 3
c)\((12x-4^3).8^3=4.8^4\)
=>\(12x-64=4.8^4:8^3\)
=>12x-64=4.8
=>12x-64=32
=>12x=96
=>x=96:12
=>x=8
Vậy x=8
d)720:[41-(2x-5)]=23.5
=>720:[41-2x-5)]=40
=>41-(2x-5)=720:40
=>41-(2x-5)=18
=>2x-5=41-18
=>2x-5=23
=>2x=23+5
=>2x=28
=>x=28:;2
=>x=14
Vậy x=14
a, 120 - 3 [ x+4]=23
3 [x+4]= 120-23 = 97
3x = 97-4
3x= 93
x= 93:3
x=31
em bt làm mỗi bài này thui mà ko bt đúng ko
a) x3 - 23 = 25 - ( 316 : 314 + 28 : 2 6 )
x3 - 23 = 25 -( 32 + 22 )
x3 - 23 = 25- ( 9 + 4 )
x3 - 23= 25 - 13
x3 - 8 = 32 - 13
x3 - 8 = 19
x3 = 19 + 8
x3 = 27
x3 = 33
=> x = 3
Vậy x =3
b) ( x2 - 1)4 = 81
( x2 - 1 )4 = 34
=> x2 - 1 = 3
x2 = 3 + 1
x2 = 4
x2 = 22
=> x = 2
Vậy x= 2
c) 5x-2 - 32 = 24 - (68 : 66 - 62 )
5x-2 - 32 = 16 - ( 62 - 62)
5x-2 - 9 = 16 - 0
5x-2 - 9= 16
5x - 2 = 16 + 9
5x - 2 = 25
5x - 2 = 52
=> x - 2 = 2
x = 2 + 2
x = 4
Vậy x = 4
d) 3x + 42 = 196 : ( 193 . 192 ) 3.12005
3x + 16 = 196 : 195 . 3 . 1
3x + 16 = 19 . 3
3x + 16 = 57
3x = 57 - 16
3x = 41
Hình như phép này đề bài sai rồi thì phải
(22+42). x + 24.5.x = 100
= ( 4 + 16 ) .x + 16 . 5 .x = 100
= 20.x + 80.x = 100
= x . ( 20 + 80) = 100
= x. 100 = 100
= x = 100:100
= x = 1
\(\left(2^2+4^2\right).x+2^4.5.x=100\)
\(\left(4+16\right).x+16.5.x=100\)
\(20.x+80.x=100\)
\(x.\left(20+80\right)=100\)
\(x.100=100\)
\(x=1\)