a) Đặt: \(A=1+2^2+2^3+...+2^{10}\)

\(\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)\)

\(\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}\)

\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)

\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)\)

\(\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)\)

\(\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045\)

Vậy: \(1+2^2+2^3+...+2^{10}=2045\)

b) 

a] \(60-3\left(x-1\right)=2^3\cdot3\)

\(\Rightarrow60-3\left(x-1\right)=24\)

\(\Rightarrow3\left(x-1\right)=36\)

\(\Rightarrow x-1=12\)

\(\Rightarrow x=13\)

b] \(\left(3x-2\right)^3=2\cdot2^5\)

\(\Rightarrow\left(3x-2\right)^3=2^6\)

\(\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3\)

\(\Rightarrow3x-2=2^2\)

\(\Rightarrow3x=6\)

\(x=2\)

c] \(5^{x+1}-5^x=500\)

\(\Rightarrow5^x\left(5-1\right)=500\)

\(\Rightarrow5^x\cdot4=500\)

\(\Rightarrow5^x=125\)

\(\Rightarrow5^x=5^3\)

\(\Rightarrow x=3\)

d] \(x^2=x^4\)

\(\Rightarrow x=x^2\)

\(\Rightarrow x-x^2=0\)

\(\Rightarrow x\left(1-x\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

giúp mình đi các bạn

- Giúp mình luôn

Bài 1: Bỏ ngoặc rồi tính (3 điểm) 

a) - (-24 + 28) + (30 - 24 + 28) 

= 24 - 28 + 30 - 24 + 28

= ( 24 - 24 ) + ( - 28 + 28 ) + 30

= 0 + 0 + 30

= 30

b) ( a + 3b - c ) + ( 2a - 3b + c )

=  a + 3b - c + 2a - 3b + c

= ( a + 2a ) + ( 3b - 3b ) + ( -c + c )

= 3b + 0 + 0

= 3b 
c) - ( -a - 2b + 2c ) + ( a - 2b + 3c) - ( a + c )

= a + 2b - 2c + a - 2b + 3c - a + c

= ( a + a - a ) + ( 2b - 2b ) + ( - 2c + c )

= a + 0 + ( - c )

= a + ( - c )

= a - c  
Bài 2: Tìm x ∈ Z; biết: (4 điểm) 

a) ( - 47 ) - (x - 28) = ( - 27 ) 

                   x - 28  = - 47 + 27

                   x - 28  = - 20

                          x  = - 20 + 28

                          x = 8

Vậy x = 8

b) (x - 1) (4 - x) = 0 
c) 23 - |5 - x| = |-13|

           |5 - x| = 23 - 13

           |5 - x| = 10

\(\Rightarrow\orbr{\begin{cases}5-x=10\\5-x=-10\end{cases}}\) 

\(\Rightarrow\orbr{\begin{cases}x=5-10=-5\\x=5+10=15\end{cases}}\)

Vậy x = - 5 hoặc x = 15
d) 8x - 3x = - 25 

           5x = - 25

             x = - 25 : 5

             x = - 5

Vậy x = - 5