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a) x . 100 + (1 + 2 + .... + 100) = 5750
x . 100 + 5050 = 5750
x . 100 = 5750 - 5050
x . 100 = 700
x = 700 : 100
x = 7
b) vô câu hỏi tương tự ấy, lười ghi quá :)))
A=4+(22+23+24+...+220)
A-4=22+23+24+...+220
2(A-4)=23+24+25+...+221
A-4=2(A-4)-(A-4)=(23+24+25+...+221)-(22+23+24+...+220)
A-4=(23-23)+(24-24)+(25-25)+...+(220-220)+(221-22)
A-4=221-4
A =221-4+4
A =221
Bạn làm tiếp nha .
a) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Rightarrow\left(x+x+x+...+x\right)+\left(1+2+3+..+100\right)=5750\Rightarrow x.100+\left(100+1\right)\cdot100:2=5750\)\
\(\Rightarrow x.100+5050=5750\Rightarrow x.100=700\Rightarrow x=7\)
b) \(\frac{x+1}{2}=\frac{8}{x+1}\Rightarrow\left(x+1\right)\left(x+1\right)=2.8\)
\(\Rightarrow\left(x+1\right)^2=16\Rightarrow\left(x+1\right)^2=4^2\)
\(\Leftrightarrow x+1=4\Rightarrow x=3\)
1.\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(\Leftrightarrow100x+5050=5750\)
\(\Leftrightarrow100x=5750-5050=700\)
\(\Leftrightarrow x=700:100=7\)
2. \(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)
\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=16\)
\(\Leftrightarrow\left(x+1\right)^2=16\)
\(\Leftrightarrow\left(x+1\right)=16:2\)
\(\Leftrightarrow\left(x+1\right)=8\)
\(\Leftrightarrow x=8-1=7\)
\(a)\) \(A=4+2^2+2^3+...+2^{20}\)
\(A=2^2+2^2+2^3+...+2^{20}\)
\(2A=2^3+2^3+2^4+...+2^{21}\)
\(2A-A=\left(2^3+2^3+2^4+...+2^{21}\right)-\left(2^2+2^2+2^3+...+2^{20}\right)\)
\(A=2^3+2^{21}-2^2-2^2\)
\(A=2^3+2^{21}-2.2^2\)
\(A=2^3+2^{21}-2^3\)
\(A=2^{21}\)
Vậy \(A=2^{21}\)
\(b)\) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow\)\(\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(\Leftrightarrow\)\(100x+\frac{100\left(100+1\right)}{2}=5750\)
\(\Leftrightarrow\)\(100x+5050=5750\)
\(\Leftrightarrow\)\(100x=5750-5050\)
\(\Leftrightarrow\)\(100x=700\)
\(\Leftrightarrow\)\(x=\frac{700}{100}\)
\(\Leftrightarrow\)\(x=7\)
Vậy \(x=7\)
Chúc bạn học tốt ~
a/(x+1)+(x+2)+...+(x+100)=5750
x+1+x+2+...+x+100=5750
100x+(1+2+...+100)=5750
100x+50.(100+1)=5750
100x+5050=5750
100x=700
x=7.
b/ 1/1.2+1/2.3+...+1/x(x+1)=2015/2016
1/1-1/2+1/3-1/4+...+1/x-1/x+1=2015/2016
1-1/x+1=2015/2016
1/x+1=1/2016
x+1=2016
x=2015
x: 3/4 = (-2)^3
x: 3/4 = -8
x= -8 * 3/4
x= -6
-------------------------------------------
135 - (7-4x) =0
7-4x = 135-0
7- 4x =135
4x = 7-135
4x = -128
x= -128 : 4
x= -32
----------------------------------
(5,6 * 2x) * 10/7 =10/7
5,6 * 2x = 10/7 : 10/7
5,6 * 2x = 1
2x = 1 : 5,6
2x = 5/28
x= 5/28 : 2
x=5/56
--------------------------------
(x+1) + (x+2) + (x+3) +...+(x+100) = 5750
100x + (1+2+3+...+100) = 5750
100x + [(1 + 99) + (2+98)...+(49 + 51) + 50 + 100] = 5750
100x + (100 * 50 + 50) = 5750
100x + 5050 = 5750
100x = 5750 - 5050
100x = 700
x=700:100
x=7
1)\(\frac{11\cdot3^{29}-9^{15}}{\left(2\cdot3^{14}\right)^2}=6\)
2)\(|2x-3|+2^3\cdot3=25\Rightarrow x=1;2\)
3) \(x183y=61831\Rightarrow x=6;y=1\)
4)\(B=\frac{n-1}{n-4}\Rightarrow n=1;3;5;7\)
5)\(\left(2x+1\right)\cdot\left(y^2-5\right)=12\Rightarrow x=1;y=3\)
mình là người đúng nhất ở bài 3 vì 61831 mới chia 2,5,9 dư 1
k cho mình nhé
a ) 5 . | x + 1 | - 3 = 20 . 2
5 . | x + 1 | - 3 = 1 . 2
5 . | x + 1 | - 3 = 2
5 . | x + 1 | = 2 + 3
5 . | x + 1 | = 5
| x + 1 | = 5 : 5
| x + 1 | = 1
\(\Rightarrow x+1\in\left\{1;-1\right\}\)
\(\Rightarrow x\in\left\{0;-2\right\}\)
Vậy \(x\in\left\{0;-2\right\}\)
b) ( x + 1 ) + ( x + 2 ) + ......... + ( x + 100 ) = 5750
[ ( x + 100 ) + ( x + 1 ) ] . [ ( x + 100 ) - ( x + 1 ) + 1 ] : 2 = 5750
[ 2x + 101 ] . 100 : 2 = 5750
[ 2x + 101 ] . 100 = 5750 . 2
[ 2x + 101 ] . 100 = 11500
[ 2x + 101 ] = 11500 : 100
[ 2x + 101 ] = 115
2x = 115 - 101
2x = 14
x = 14 : 2
x = 7
Vậy x = 7
c) ( 52 - 1 ) . 3 - 2 = 70
( 25 - 1 ) . 3 = 70 + 2
24 . 3 = 72
72 = 72
Câu 2:
\(x^2=9\)
\(x^2=3\)
\(\left[\begin{array}{l}x=-3\\ x=3\end{array}\right.\)
vậy: \(x\in\) {-3; 3}