\(9^x:3^{x+9}=27\)   

\(9^x=27\cdot3^{x+9}\)   

\(\left(3^2\right)^x=3^3\cdot3^{x+9}\)   

\(3^{2x}=3^{x+12}\)   

\(\Rightarrow2x=x+12\)   

\(2x-x=12\)   

\(x=12\)   

\(4^{x+y}:2^{5y}=32\)   

\(4^{12+y}=32\cdot2^{5y}\)   

\(\left(2^2\right)^{12+y}=2^5\cdot2^{5y}\)   

\(2^{24+2y}=2^{5+5y}\)   

\(24+2y=5+5y\)   

\(24-5=5y-2y\)   

\(3y=19\)   

\(y=19:3\)   

\(y=\frac{19}{3}\)   

Vậy \(x=12;y=\frac{19}{3}\)

\(\left(x+y\right)^3=12x+3\)lẻ\(\Rightarrow x+y\)lẻ

\(\left(x+y\right)^3=12x+3< 12x+12y\Rightarrow\left(x+y\right)^2< 12< 4^2\)

\(\Rightarrow x+y< 4\). Do đó: x+y=3

Ta có: 12x+3=27=> x=2 nên y=1

Đặt \(A=1+2+2^2+2^3+...+2^{20}\)

\(2A=2+2^2+2^3+2^4+...+2^{21}\)

\(2A-A=\left(2+2^2+2^3+...+2^{21}\right)-\left(1+2+2^2+...+2^{20}\right)\)

\(A=2^{21}-1\)

Ta đặt 

A= 1+2^1+2^2+2^3+....2^20

2A= 2¹+2²+2³+....+2²¹

=>2A-A=(2^1+2^2+2^3+...+2^21)-(1+2^2+2^3+...)

1A=2^21-1

Vậy A=2^21-1

1) \(541+\left(218-x\right)=375\)

\(\Leftrightarrow759-x=375\)

\(\Leftrightarrow x=384\)

2) \(5\cdot\left(x+35\right)=515\)

\(\Leftrightarrow x+35=103\)

\(\Rightarrow x=68\)

3) \(96-3\cdot\left(x+1\right)=42\)

\(\Leftrightarrow3\cdot\left(x+1\right)=54\)

\(\Leftrightarrow x+1=18\)

\(\Rightarrow x=17\)

4) \(2\cdot x-138=2^3\cdot3^2\)

\(\Leftrightarrow2\cdot x-138=72\)

\(\Leftrightarrow2\cdot x=210\)

\(\Rightarrow x=105\)

Tính ra thôi

a) \(1^3+2^3=1+8=9=3^2\)

Vậy tổng 1³ + 2³ là 1 số chính phương

b) \(1^3+2^3+3^3=9+27=36=6^2\)

Vậy tổng 1³ + 2³ + 3³ là 1 số chính phương

c) \(1^3+2^3+3^3+4^3=36+64=100=10^2\)

Vậy tổng 1³ + 2³ + 3³ + 4³ là 1 số chính phương

Answers:

1. A

2. A

3. B

4. D

5. B

6. B

7. D

8. C

9. D

10. A

11. B

12. B

13. B

14. A

15. B

16. B

17. D

18. A

19. B

20. A

21. B

22. B

23. A

24. B

25. D

1. My sister is very fond .................... chocolate candy.

A. of

B. about

C. with

D. at

2. I have studied English ....................eight months.

A. for

B. since

C. by

D. in

3. Listen ....................our teacher !

A. with

B. to

C. for

D. in

4. There isn’t ....................food in the house.

A. none

B. no

C. some

D. any

5. He arrives …………………..at six o’clock.

A. at home

B. home

C. in home

D. to home

6. Herbert has had his car………………….. 1999.

A. ago

B. since

C. to

D. for

7. How long will it ....................to get there ?

A. cost

B. lose

C. make

D. take

8. I ....................it to you if you don’t have one.

A. give

B. gave

C. will give

D. would give

9. ....................your homework yet ?

A. Did you finished

B. Are you finishing

C. Do you finish

D. Have you finished

10. It’s the best book I …………………..read.

A. have ever

B. had ever

C. will ever

D. can ever

11. He looked very..................when I told him the news.

A. happily

B. happy

C. happiness

D. was happy

12. She is ..................in history.

A. interests

B. interested

C. interesting

D. being interest

13. Is the Eiffel Tower taller....................Big Ben ?

A. then

B. than

C. as

D. of

14. At school, David was..................anyone else in his class.

A. as clever as

B. as clever than

C. cleverer as

D. cleverest

15. She speaks French ....................than you.

A. more faster

B. more fluently

C. well

D. the most fluently

16. It began to rain while we…………………..soundly.

A. slept

B. were sleeping

C. have slept

D. are sleeping

17. She doesn’t coffee, does she ?

A. Yes, she doesn’t

B. No, she does

C. Yes, she did

D. No, she doesn’t

18. I won't go to bed …………………..I finish my homework.

A. until

B. when

C. while

D. since

19. Is this book ………………….. ? Yes, it's mine.

A. you're

B. yours

C. you

D. your

20. …………………..do you come to school ? By bus

A. How

B. What

C. By

D. When

21. Why do people usually sing ?
A. They birds. B. They feel happy.
C. They want to tell a story . D. They lik e studying music.

22. Which birds sing the most beautiful songs ?

A. Birds in a good temper.

B. Cock birds.

C. Hen birds.

D. Female birds which attract male birds.

23. What warnings does a bird sometimes sing ?

A. A warning to keep away.

B. A warning to come quickly.

C. A warning about the approach of people

D. A warning to stop singing.

24. What do most birds usually do if they cannot sing well ?

A. warn other birds to go away.

B. give their information in another way.

C. find a wife.

D. fly high in the sky.

25. What is one bird's unusual way of attracting a hen bird ?

A. It dances.

B. It spreads out its tail.

C. It searches for a wife.

D. It uses shells and flowers to make a garden.

(60+30):2=45(km/giờ)

       van to trung binh tu A den B la :

           (  60+30 ) : 2 = 45  km\h 

                Dap so : 45 km\h

3² . 5³ - 20{300 - [540 - 2³ (7⁸ : 7⁶ + 7⁰)]}

= 9 . 125 - 20{300 - [540 - 8(7² + 7⁰)]}

= 9 . 125 - 20{300 - [540 - 8(49 + 1)]

= 9 . 125 - 20{300 - [540 - 8.50]

= 9 . 125 - 20{300 - [540 - 400]}

= 9 . 125 - 20{300 - 140}

= 9 . 125 - 20. 160

= 1125 - 3200 = -2075

\(=9\cdot125-20\cdot\left\{300-\left[540-8\cdot\left(7^2+1\right)\right]\right\}\)   

\(=1125-20\cdot\left\{300-\left[540-8\cdot\left(49+1\right)\right]\right\}\)   

\(=1125-20\cdot\left[300-\left(540-8\cdot50\right)\right]\)   

\(=1125-20\cdot\left[300-\left(540-400\right)\right]\)   

\(=1125-20\cdot\left(300-140\right)\)   

\(=1125-20\cdot160\)    

\(=1125-3200\)    

\(=-2075\)

Ta có : A = 2 + 2² + 2³ + ... + 2²⁰²¹

=> 2A = 2² + 2³ + 2⁴ + ... + 2²⁰²²

Khi đó 2A - A = (2² + 2³ + 2⁴ + ... + 2²⁰²²) - (2 + 2² + 2³ + ... + 2²⁰²¹)

                A = 2²⁰²² - 2

b) Ta có A + 2 = 2²⁰²² - 2 + 2 = 2²⁰²² => A + 2 là lũy thừa của 2

c) Ta có A + 2 = 2^{x + 1}

=> 2²⁰²² = 2^{x + 1}

=> x + 1 = 2022

=> x = 2021

d) Ta có 3.2²⁰²² = (2 + 1).2²⁰²² = 2²⁰²³ + 2²⁰²² > 2²⁰²² - 2 = A 

Vậy  3.2²⁰²² > A 

a) A = 2 + 2² + 2³ + ... + 2²⁰²¹

=> 2A = 2² + 2³ + ... + 2²⁰²²

=> A = 2A - A

         = 2² + 2³ + ... + 2²⁰²² - ( 2 + 2² + 2³ + ... + 2²⁰²¹ )

         = 2² + 2³ + ... + 2²⁰²² - 2 - 2² - 2³ - ... - 2²⁰²¹ 

         = 2²⁰²² - 2

b) Ta có A + 2 = 2²⁰²² - 2 + 2 = 2²⁰²² ( đpcm )

c) A + 2 = 2^x+1

<=> 2²⁰²² - 2 + 2 = 2^x+1

<=> 2²⁰²² = 2^x+1

<=> 2022 = x + 1

<=> x = 2021

d) Ta có3.2²⁰²² = (1+2).2²⁰²² = 2²⁰²² + 2²⁰²³ > 2²⁰²² - 2

=> 3.2²⁰⁰² > A

(2x - 1)⁶ = (2x - 1)⁴

=> (2x - 1)⁶ - (2x - 1)⁴ = 0

=> (2x - 1)⁴.[(2x - 1)² - 1] = 0

=> \(\orbr{\begin{cases}\left(2x-1\right)^4=0\\\left(2x-1\right)^2-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}2x-1=0\\\left(2x-1\right)^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}2x-1=0\\2x-1=\pm1\end{cases}}\)

Khi 2x - 1 = 0 => x = 1/2

Khi 2x - 1 = -1 => x = 0

Khi 2x - 1 = 1 => x = 1

Vậy \(x\in\left\{\frac{1}{2};0;1\right\}\)là giá trị cần tìm

( 2x - 1 )⁶ = ( 2x - 1 )⁴

<=> ( 2x - 1 )⁶ - ( 2x - 1 )⁴ = 0

<=> ( 2x - 1 )⁴[ ( 2x - 1 )² - 1 ] = 0

<=> \(\orbr{\begin{cases}\left(2x-1\right)^4=0\\\left(2x-1\right)^2-1=0\end{cases}}\)

<=> \(\hept{\begin{cases}x=\frac{1}{2}\\x=1\\x=0\end{cases}}\)( thay = dấu hoặc hộ nhé )