\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\cdot\cdot\cdot+\left(x+100\right)=5750\)

\(\Rightarrow\left(x+x+x+\cdot\cdot\cdot+x\right)+\left(1+2+3+\cdot\cdot\cdot+100\right)=5750\) (1)

Đặt \(A=1+2+3+\cdot\cdot\cdot+100\)

Số các số hạng trong \(A\) là: \(\left(100-1\right):1+1=100\left(số\right)\)

Tổng \(A\) bằng: \(\left(100+1\right)\cdot100:2=5050\)

Khi đó, (1) trở thành:

\(100x+5050=5750\)

\(\Rightarrow100x=5750-5050\)

\(\Rightarrow100x=700\)

\(\Rightarrow x=\dfrac{700}{100}=7\left(tm\right)\)

Vậy \(x=7\).

(x+1)+(x+2)+...+(x+100)=5750

=>x+x+...+x+1+2+3+...+100=5750

=>100x+5050=5750

=>100x=700

=>x=7

=>100x+1+2+..+100=5750

=>100x+\(\frac{\left(100+1\right)100}{2}\)=5750

=>100x+5050=5750

=>100x=700

=>x=7

( x + 1 ) + ( x + 2 ) + ( x + 3 ) + .....+ ( x + 100 ) = 5750

(100.x)+(1+2+3+.........+100)=5750

100.x+101.50=5750

100x+5050=5750

100.x=700

x=700:100

x=7

a: =>41-(2x-5)=720:40=18

=>2x-5=23

=>2x=28

=>x=14

b: =>100x+5050=5750

=>100x=700

=>x=7

a: =>41-(2x-5)=720:40=18

=>2x-5=23

=>2x=28

=>x=14

b: =>100x+5050=5750

=>100x=700

=>x=7

a) Dãy trên có số số hạng là :

( x - 1 ) : 1 + 1 = ( x - 1 ) + 1 = x 

=> 1 + 2 + 3 + 4 + ... + x = 45

=> ( x + 1 ) . x : 2  = 45

=> ( x + 1 ) . x = 90

=> ( x + 1 ) . x = 10 . 9

=> x = 9

Vậy x = 9

a) Dãy trên có số số hạng là :

( x - 1 ) : 1 + 1 = ( x - 1 ) + 1 = x 

=> 1 + 2 + 3 + 4 + ... + x = 45

=> ( x + 1 ) . x : 2  = 45

=> ( x + 1 ) . x = 90

=> ( x + 1 ) . x = 10 . 9

=> x = 9

Vậy x = 9

b) ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 100 ) = 5750

=> ( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750 ( mỗi nhóm có 100 số hạng )

=> 100x + ( 100 + 1 ) . 100 : 2 = 5750

=> 100x + 5050 = 5750

=> 100x = 700

=> x = 7

Vậy x = 7

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.   \(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)

\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=16\)

\(\Leftrightarrow\left(x+1\right)^2=16\)

\(\Leftrightarrow\left(x+1\right)=16:2\)

\(\Leftrightarrow\left(x+1\right)=8\)

\(\Leftrightarrow x=8-1=7\)

Bạn sửa lại chỗ bài 2. Ở chỗ:

\(\left(x+1\right)^2=16\) và các chỗ sau chỗ đó thành:

\(\left(x+1\right)^2=16\)

\(\Leftrightarrow\left(x+1\right)^2=4^2\)

\(\Leftrightarrow x+1=4\)

\(\Leftrightarrow x=4-1=3\)