(x + 1) + (x + 2) + ...+(x + 2013) = 0

=> 2013x + ( 1 + 2 + 3 + .... + 2013 ) = 0

Áp dụng công thức tính dãy số ta có :

\(1+2+3+....+2013=\frac{\left[\left(2013-1\right):1+1\right].\left(2013+1\right)}{2}=\frac{2013.2014}{2}=2027091\)

=> 2013x + 2027091 = 0

=> 2013x = -2027091

=> x = -1007

( x + 1 ) + ( x + 2 ) + ... + ( x + 2013 ) = 0

( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 2013 ) = 0

2013x + 2027071 = 0

2013x = 0 - 2027071

2013x = -2027071

x = ( -2027071 ) : 2013

Tự tính nhé

2013x+(1+2+...+2013)=0

2013x+2027091         =0

2013x                       =0-2027091=-2027091

x                              =-2027091:2013=-1007

Bài 1 :

a) \(A=\left(x-3\right)^2-\left(x-5\right)\left(x+5\right)\)

\(A=x^2-6x+9-x^2+25\)

\(A=34-6x\)

b) \(B=2\left(x+y\right)\left(x-y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)

Dễ thấy đây là HĐT thứ 1

\(B=\left(x+y+x-y\right)^2\)

\(B=\left(2x\right)^2\)

\(B=4x^2\)

Bài 2 :

a) \(2x\left(x+5\right)-x^2-5x=0\)

\(2x\left(x+5\right)-x\left(x+5\right)=0\)

\(\left(x+5\right)\left(2x-2\right)=0\)

\(2\left(x+5\right)\left(x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+5=0\\x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-5\\x=1\end{cases}}}\)

b) \(4x\left(x-2013\right)-x+2013=0\)

\(4x\left(x-2013\right)-\left(x-2013\right)=0\)

\(\left(x-2013\right)\left(4x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-2013=0\\4x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=2013\\x=\frac{1}{4}\end{cases}}}\)

x chỉ bằng 2013 thôi vì 0+0=0

x=-1007 nha bạn

(x+1)+(x+2)+.........+(x+2013)=0

=>x+1+x+2+........+x+2013=0

=>(x+x+.........+x)+(1+2+............+2013)=0

=>2013x+2013.(2013+1):2=0

=>2013x+2027091=0

=>2013x=0-2027091

=>2013x=-2027091

=>x=2027091:2013

=>x=-1007

Đáp số là 1007 nha!

a) ( 2x - 1 )( 2x + 1 ) - 4( x² + x ) = 16

⇔ 4x² - 1 - 4x² - 4x = 16

⇔ -4x - 1 = 16

⇔ -4x = 17

⇔ x = -17/4

b) 5x( x - 2013 ) - x + 2013 = 0

⇔ 5x( x - 2013 )  - ( x - 2013 ) = 0

⇔ ( x - 2013 )( 5x - 1 ) = 0

⇔ \(\orbr{\begin{cases}x-2013=0\\5x-1=0\end{cases}}\)

⇔ \(\orbr{\begin{cases}x=2013\\x=\frac{1}{5}\end{cases}}\)

a) \(\left(2x-1\right)\left(2x+1\right)-4.\left(x^2+x\right)=16\)

\(4x^2-1-4x^2-4x=16\)

\(-1-4x=16\)

\(-4x=17\)

\(x=-\frac{17}{4}\)

b) \(5x\left(x-2013\right)-x+2013=0\)

\(\left(x-2013\right)\left(5x-1\right)=0\)

\(\Rightarrow\hept{\begin{cases}x-2013=0\\5x-1=0\end{cases}\Rightarrow\hept{\begin{cases}x=2013\\x=\frac{1}{5}\end{cases}}}\)

a) \(\left(2x-1\right)\left(2x+1\right)-4\left(x^2+x\right)=16\)

\(\Leftrightarrow4x^2-1-4x^2-4x=16\)

\(\Leftrightarrow-1-4x=16\)\(\Leftrightarrow4x=-17\)\(\Leftrightarrow x=-\frac{17}{4}\)

Vậy \(x=-\frac{17}{4}\)

b) \(5x\left(x-2013\right)-x+2013=0\)

\(\Leftrightarrow5x\left(x-2013\right)-\left(x-2013\right)=0\)

\(\Leftrightarrow\left(x-2013\right)\left(5x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-2013=0\\5x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2013\\5x=1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2013\\x=\frac{1}{5}\end{cases}}\)

Vậy \(x=2013\)hoặc \(x=\frac{1}{5}\)

a) Ta có 

1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/x - 1/x + 2 = 5

rút gọn ta được : 1 - 1/x+2 = 5

<=> x + 2 - 1 / x+ 2

<=> x + 1 / x + 2 = 5

<=> x+ 1 = 5x + 10

<=> - 4x = 9

<=> x = -9/4

B) / x +4/ = 2^0 + 1 ^ 2013

=> /x + 4/ = 1 + 1

=> / x + 4 / = 2

TH 1 :  x+ 4 = 2

 => x = 2 - 4 = -2

TH2 : x + 4 = -2

=> x = -2 - 4 = -6

=> x = { - 2 , -6 }

1) x-1998=2002

x=2002+1998

x=4000

2)x-2012=2013

x=2012+2013

x=4025

3)x:18=25

x=25.18

x=450

4)x:23=72

x=72.23

x=1656

5)(135+2012).x=0

x=0:(135+2012)

x=0

6)x.(1972+2013)=0

x=0:(1972+2013)

x=0

7)x.(x-1)=0

<=> x=0 hoặc x-1=0

x-1=0

x=0+1

x=1

Vậy x=1 hoặc 0

8) (x-9).(x-15)=0

<=> x-9=0 hoặc x-15=0

x-9=0

x=9

x-15=0

x=15

Vậy x=9 hoặc x=15

chúc bạn học tốt nha

1) X=4000                 2)X=4025                          3)X=450             4)X=1656      5)X=0   6) X=0             7)X=0 ,X=1      8)X=9,X=15

1) x - 1998 = 2002                                    2) x - 2012 = 2013                        3) x : 18 = 25                    4) x : 23 = 72

              x  = 2002 + 1998                                      x   = 2013 + 2012                      x  = 25 x 18                      x  = 72 x 23

              x  = 4000                                                  x   = 4025                                  x  =  450                           x  = 1656