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\((x+1)+(x+2)+(x+3)+...+(x+100)=570\)
\(\Rightarrow(x+x+x+...+x)+(1+2+3+...+100)=570\)
\(\Rightarrow100x+\frac{(1+100)\cdot100}{2}=570\)
\(\Rightarrow100x+5050=570\)
\(\Rightarrow100x=570-5050\)
\(\Rightarrow100x=-4480\)
\(\Rightarrow x=-44,8\)
P/S : Làm bừa :> Hoq chắc
giải giúp mik với a) 2^x+1 =64
b) 570-x: 3 và 17<x<20
c) (4x-9)-(x+111)=0
giúp mik với nha mik cần gấp
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\(a,2^{x+1}=64\\ \Rightarrow a,2^{x+1}=2^6\\ \Rightarrow x+1=6\\ \Rightarrow x=5\)
\(b,x=18\)
\(c,\left(4x-9\right)-\left(x+111\right)=0\\ \Rightarrow4x-9-x-111=0\\ \Rightarrow3x-120=0\\ \Rightarrow3x=120\\ \Rightarrow x=40\)
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b/ x + (x + 1) + (x + 2) + .... + (x + 30) = 1240
x + (x + x + ....+ x) + (1 + 2 + ... + 30) = 1240
x + 30x + 465 = 1240
31x = 1240 - 465
31x = 775
=> x = 775 : 31 = 25
c/ Sửa đề (x + 4) + (x + 6) + (x + 8) + .... + (x + 26) = 210
(x + x + x + .... + x) + (4 + 6 + 8 + .... + 26) = 210
12x + 180 = 210
12x = 210 - 180 = 30
=> x = 30 : 12 = 2,5
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a: S=1(1+1)+2(1+2)+...+100(1+100)
=1+2+...+100+1^2+2^2+...+100^2
\(=\dfrac{100\cdot102}{2}+\dfrac{100\cdot\left(100+1\right)\cdot\left(2\cdot100+1\right)}{6}\)
\(=100\cdot51+\dfrac{100\cdot101\cdot201}{6}\)
=343450
b: \(A=1\cdot2\cdot3+2\cdot3\cdot4+...+100\cdot101\cdot102\)
=>\(4\cdot A=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\left(5-1\right)+...+100\cdot101\cdot102\left(103-99\right)\)
=>4*A=100*101*102*103
=>A=25*101*102*103
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a)x+(x+1)+(x+2)+(x+3)+...+(x+99)+(x+100)=5555
=> 101x +5050 = 5555
=> 101x = 505
=> x = 505 : 101 = 5
Vậy, x = 5
b)1+2+3+4+...+x=820
=> ( x+1) x :2 = 820
=> (x+1)x = 1640
Mà 1640 = 40 . 41
=> x = 40 ( vì {x+1} - x = 1)
Vậy, x = 40
c) 3x+1 = 9.27=243
=> 3x+1 = 35
=>x + 1 = 5
=> x = 4
Vậy, x=4
d) x+2x+3x+...+99x+100x=15150
=> [( 100 + 1) x 100 :2 ] x = 15150
=> 5050x = 15150
=> x = 15150:5050 = 3
Vậy, x =3
e)(x+1)+(x+2)+(x+3)+...+(x+100)=205550
=> 100x + 5050 = 205550
=> 100x = 205550 - 5050= 200500
=> x = 200500 : 100 = 2005
Vậy, x = 2005
f)3x+3x+1+3x+2=351
=> 3x + 3x . 3 + 3x x 9 = 351
=> 3x ( 1+3+9) = 351
=> 3x . 13 = 351
=> 3x = 351 :13=27 mà 27 = 33
=> x=3
Vậy, x=3
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a) x - 12 = 14 x = 14 + 12 x = 26
b) 2 x - 13 = 3 . 17 2 x = 51 + 13 2 x = 64 x = 64 : 2 x = 32
c) x - 43 = 2 . 18 x = 36 + 43 x = 79
d) x - 14 . 39 = 0 x - 14 = 0 x = 14
e) 13 - x . 28 = 28 13 - x = 28 : 28 13 - x = 1 x = 13 - 1 x = 12
f) 22 . 35 - x = 22 35 - x = 1 x = 35 - 1 x = 34
g) x - 24 : 2 = 18 x - 12 = 18 x = 39
h) 400 + 275 - x = 570 275 - x = 570 - 400 275 - x = 170 x = 275 - 170 x = 105
( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ..... + ( x + 100 ) = 570
x + 1 + x + 2 + x + 3 + ...... + x + 100 = 570
x . 100 + ( 1 + 2 + 3 + .... + 100 ) = 570
x . 100 + { ( 100 + 1 ) x [ ( 100 - 1 ) : 1 + 1 ] : 2 = 570
x . 100 + ( 101 x 100 : 2 ) = 570
x . 100 + ( 10100 : 2 ) = 570
x . 100 + 5050 = 570
x . 100 = 570 - 5050
x . 100 = -4480
x = -4480 : 100
x = -44,8
Vậy x = -44,8
Đề bài thế này mới đúng nè :
(x + 1) + (x + 2) + (x + 3) + .... + (x + 100) = 5750
=> 100x + (1 + 2 + 3 + ... + 100) = 5750
=> 100x + 5050 = 5750
=> 100x = 5750 - 5050
=> 100x = 700
=> x = 700 : 100
=> x = 7