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

a) \(\frac{3}{4}+\frac{2}{5}x=\frac{29}{60}\)

\(\frac{2}{5}x=\frac{29}{60}-\frac{3}{4}\)

\(\frac{2}{5}x=\frac{-4}{15}\)

\(x=\frac{-4}{15}:\frac{2}{5}\)

\(x=\frac{-2}{3}\)

b) \(x^4=16\)

\(x^4=2^4\)

\(x=2\)

c) \(\left(x+5\right)^3=-64\)

\(\left(x+5\right)^3=-4^3\)

\(x+5=-4\)

\(x=-4-5\)

\(x=-9\)

d) \(\left(x-\frac{3}{4}\right)^2=0\)

\(\left(x-\frac{3}{4}\right)^2=0^2\)

\(x-\frac{3}{4}=0\)

\(x=0+\frac{3}{4}\)

\(x=\frac{3}{4}\)

e) \(x:8,5=0,69:\left(-1,15\right)\)

\(x:8,5=-0,6\)

\(x=-0,6.8,5\)

\(x=-5,1\)

A.2/5x=29/60-3/4

2/5x=29/60-45/60

2/5x=-4/15

x=-4/15:2/5

x=4/15.5/2 

x=-2/3

B. x mũ 4 = 42

-) x=2

C. (x+5) mũ 3 = -4 3

x+5 = -4

X= -4-5

X=-9

D. ( X -3/4)mũ 2=0 mũ 2

X= 0+3/4

X=3/4

E. X:8,5=-0,6

X=-0,6*8,5

X=5,1

Bài 2: 

a: \(\Leftrightarrow x=\dfrac{29}{60}\cdot\dfrac{-7}{5}=\dfrac{-203}{300}\)

b: \(\Leftrightarrow x\cdot\dfrac{2}{5}=\dfrac{29}{60}-\dfrac{3}{4}=\dfrac{29-45}{60}=\dfrac{-16}{60}=\dfrac{-8}{30}\)

\(\Leftrightarrow x=\dfrac{-8}{30}:\dfrac{2}{5}=\dfrac{-8\cdot5}{30\cdot2}=\dfrac{-40}{60}=-\dfrac{2}{3}\)

1. a, 15-(3+x)+2x=19
=> 15- 3 - x + 2x = 19
=> -x + 2x = 19 - 15 +3
=> ( -1 + 2 )x = 7
=> x = 7
b, (-58)-(19-58-x)=60
=> (-58)-(-39-x)=60
=> -58 +39 + x = 60
=> -19 + x = 60
=> x = 60 - (-19) = 79
c, 2(x-4)-3(x+5)=4
=> (2x - 8 )-(3x+15)= 4
=> 2x - 8 - 3x - 15 = 4
=> 2x - 3x = 4 + 15 + 8
=> - x = 27
=> x = -27
d, (2-3x)+(x-3)=(5x-1)-(5x-2)
=> 2 - 3x + x - 3 = 5x - 1 - 5x + 2
=> 2 - 3 - 3x + x = 5x - 5x - 1 +2
=> 2 - 3 - 3x + x = 1
=> - 3x + x = 1 - 2 + 3
=> -2x = 2
=> x= -1
=))))

2.

a,

A= -3752-(29-3632)-51

A= -3572-29+3632-51

A=(-3572+3632)-29-51

A=

1> a, 15 - ( 3 + x ) + 2 x = 19
=> 15 - 3 - x + 2x = 19
=> -x + 2x = 19 - 15 +3
=> ( -1 + 2 ) x = 7
=> x = 7
b, ( -58 ) - ( 19-58-x ) = 60
=> ( -58 ) - ( -39 – x ) = 60
=> -58 + 39 + x = 60
=> -19 + x = 60
=> x = 60 - ( -19 ) = 79
c, 2 ( x - 4 ) - 3 ( x+5 ) = 4
=> ( 2x - 8 ) - ( 3x + 15 ) = 4
=> 2x - 8 - 3x - 15 = 4
=> 2x - 3x = 4 + 15 + 8
=> - x = 27
=> x = -27
d, ( 2 - 3x ) + ( x - 3 ) = ( 5x - 1 ) - ( 5x – 2 )
=> 2 - 3x + x - 3 = 5x - 1 - 5x + 2
=> 2 - 3 - 3x + x = 5x - 5x - 1 +2
=> 2 - 3 - 3x + x = 1
=> - 3x + x = 1 - 2 + 3
=> -2x = 2
=> x= -1

D

D

D

\(\left(5x-29\right)-\left(2x-29\right)=-21\)

\(5x-29-2x+29=-21\)

\(5x-2x=-21+29-29\)

\(3x=-21\)

\(x=-7\)

C

C

C