\((x+1)+(x+2)+(x+3)+...+(x+100)=570\)

\(\Rightarrow(x+x+x+...+x)+(1+2+3+...+100)=570\)

\(\Rightarrow100x+\frac{(1+100)\cdot100}{2}=570\)

\(\Rightarrow100x+5050=570\)

\(\Rightarrow100x=570-5050\)

\(\Rightarrow100x=-4480\)

\(\Rightarrow x=-44,8\)

P/S : Làm bừa :> Hoq chắc 

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=570\)

\(\left(x+x+x+...+x\right)+\left(1+2+...+100\right)=570\)

\(100x+5050=570\)

\(100x=-4480\)

\(x=-44,8\)

chịu

1) PT \(\Leftrightarrow\left(\dfrac{x+1}{35}+1\right)+\left(\dfrac{x+3}{33}+1\right)=\left(\dfrac{x+5}{31}+1\right)+\left(\dfrac{x+7}{29}+1\right)\)

\(\Leftrightarrow\dfrac{x+36}{35}+\dfrac{x+36}{33}=\dfrac{x+36}{31}+\dfrac{x+36}{29}\)

\(\Leftrightarrow\left(x+36\right)\left(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}\right)=0\)

\(\Leftrightarrow x+36=0\) (Do \(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}>0\))

\(\Leftrightarrow x=-36\).

Vậy nghiệm của pt là x = -36.

2) x(x+1)(x+2)(x+3)= 24

⇔ x.(x+3)  .   (x+2).(x+1)  = 24

⇔(\(x^2\) + 3x) . (\(x^2\) + 3x + 2) = 24

Đặt \(x^2\)+ 3x = b

⇒ b . (b+2)= 24

Hay: \(b^2\) +2b = 24

⇔\(b^2\) + 2b + 1 = 25

⇔\(\left(b+1\right)^2\)= 25

+ Xét b+1 = 5 ⇒ b=4 ⇒  \(x^2\)+ 3x = 4 ⇒ \(x^2\)+4x-x-4=0 ⇒x(x+4)-(x+4)=0

⇒(x-1)(x+4)=0⇒x=1 và x=-4

+ Xét b+1 = -5 ⇒ b=-6 ⇒ \(x^2\)+3x=-6 ⇒\(x^2\) + 3x + 6=0

⇒\(x^2\) + 2.x.\(\dfrac{3}{2}\) + (\(\dfrac{3}{2}\))² = - \(\dfrac{15}{4}\)  Hay ( \(x^2\) +\(\dfrac{3}{2}\) )²= -\(\dfrac{15}{4}\) (vô lí)

⇒x= 1 và x= 4

ghi rõ đề please

cách giải như sau:31-30=1,29-28=1.Chúng ta sẽ chia ra các cặp như sau:31,29,27,25,23,21,19,17,15,13,11,9,7,5,3,1 và mỗi cặp tương ứng là 1.Chúng ta có 16 cặp là 16 cộng thêm 1 nữa là 17.Đáp số:17

1: Ta có: 7x+6(3-x)=27-20+73

\(\Leftrightarrow7x+18-6x=80\)

\(\Leftrightarrow x=80-18=62\)

Vậy: x=62

2: Ta có: \(6x-5\left(x-7\right)=\left(27-514\right)-486-73\)

\(\Leftrightarrow6x-5x+35=27-514-486-73\)

\(\Leftrightarrow x+35=-1046\)

\(\Leftrightarrow x=-1081\)

Vậy: x=-1081

thanks you

a) / 2x + 1 / = 7

=>2x+1 thuộc {-7;7}

+)2x+1=7=>2x=6=>x=3

+)2x+1=-7=>2x=-8=>x=-4

vậy x thuộc {3;-4}

b) 3/x + 1 / + 1 = 27

=>3/x+1/=27-1=26

=>/x+1/=26:3=26/3

=>x+1 thuộc {-26/3; 26/3}

+)x+1=26/3=>x=26/3 - 1 = 23/3

+)x+1=-26/3=>x=-26/3 - 1=-29/3

vậy x thuộc {-29/3; 23/3}

5 ( năm )

a, <=> (x-5/100) -1 +(x-4/101) -1 +(x-3/102) -1= (x-100/5) -1+(x-101/4) -1 +(x-102/3) -1
<=> (x-105)(1/100 +1/101 +1/102)= (x-105)(1/5+1/4+1/3)
<=> (x-105)(1/100+1/101+1/102-1/5-1/4-1/3)=0
vì 1/100+1/101+1/102-1/5-1/4-1/3 khác 0 <=> x-105=0
<=> x=105

b, 29-x/21 +1+27-x/23 +1+25-x/25 +1+23-x/27 +1+21-x/29 +1=0
<=> 50-x/21 +50-x/23 +50-x/25 +50-x/27 +50-x/29=0
<=> (50-x)(1/21 +1/23 +1/25 +1/27 +1/29)=0
vì 1/21+1/23+1/25+1/27+1/29 lớn hơn 0
nên 50-x=0
<=> x=50