Mục tiêu của em là đỗ vào trường Chuyên cấp 3!!!

a) ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\b>0\\a\ne b\end{matrix}\right.\)

P = \(\dfrac{a-\sqrt{ab}+b+3\sqrt{ab}}{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}.\left[\left(\dfrac{a+\sqrt{ab}+b-3\sqrt{ab}}{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}\right):\dfrac{a-b}{a+\sqrt{ab}+b}\right]\)= \(\dfrac{\left(\sqrt{a}+\sqrt{b}\right)^2}{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}.\left[\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}.\dfrac{a+\sqrt{ab}+b}{a-b}\right]\)

= \(\dfrac{\sqrt{a}+\sqrt{b}}{a-\sqrt{ab}+b}.\dfrac{\sqrt{a}-\sqrt{b}}{a-b}\)

= \(\dfrac{1}{a-\sqrt{ab}+b}\)

b) có a = 16 và b = 4 (thoả mãn ĐKXĐ)

Thay a = 16, b =4 vào P có:

P = \(\dfrac{1}{16-\sqrt{16.4}+4}\)= \(\dfrac{1}{12}\)

Vậy tại a =16, b = 4 thì P = \(\dfrac{1}{12}\)

Chào mọi người ạ! Cũng sắp đến tết rồi nhỉ, lại một năm đã qua với biết bao kỉ niệm và cảm xúc. Mình rất thích gửi gắm những tâm tư, tình cảm cùng với những kỉ niệm đẹp vào trong những trang sách. Mình muốn review cho mn quyển sách mà mình thực sự rất tâm đắc, đọc đi đọc lại không thấy chán, đó là "Chẳng có mùa đông nào không thể vượt qua." của Ban Mã.

"Gió lạnh mùa đông phóng đại mọi nỗi sợ hãi. Sợ trời dần chuyển rét, sợ bầu trời âm u xám xịt, sợ tiếng gió rít vào thanh cửa mang hơi lạnh về. Sợ một mình qua đường giữa phố, người với người ai cũng có tay đan. May mà mùa đông rất ngắn ngủi. Vượt qua được những thời điểm khó khăn nhất, nó sẽ trở thành quá khứ đã xa.

                     Bởi, chẳng có mùa đông nào không thể vượt qua."

Chính câu nói ấy của tác giả Ban Mã đã khơi lên trong tôi sự tò mò mãnh liệt về cuốn sách ấy, hay về chính tâm hồn tác giả. Hãy đọc thử đi, và bạn sẽ không bao giờ cảm thấy hối tiếc khi đã chi tiêu thời gian cho cuốn sách ấy.

Mùa đông thật ngắn ngủi, và chúng ta sắp vượt qua mùa đông để tiến tới một mùa xuân thắm tươi nồng nàn tràn đầy hạnh phúc. Hi vọng mọi người sẽ hạnh phúc an khang bên người thân, ngồi bên nồi bánh chưng mà ngắm nhìn tiết trời mùa xuân tươi đẹp sau một mùa đông của năm cũ đầy khó khăn và thử thách. Happy new year!

1. I regretted not asking for his name and address.

2. The coach told them that it was time they had begun training for their next match.

3. I said that it wasn't so foggy that day as it had been the previous day.

4. I advised Jerry to take an umbrella as it was pouring with rain.

5. I told her that it was kind of her to look after my mother so well.

6. I said that that used to be a busy street but then it wasn't.

7. Peter exclaimed that Mary had a beautiful dress.

8. Mr. Minh asked Hai to leave early.

9. His colleagues said that he had been leaking information to the Press and he denied it.

10. He wishes I had a nice sleep. 

1. Ha asked Nam where he was working then.

2. We haven't visited our old school since we went to HCM City.

3. I spent 2 hours doing the test at school yesterday.

1. I have just been here, so I don't know how to go to the market.

-> Because I have just been here, I don't know how to go to the market.

2. It was too hot for us to go out.

-> Because it was too hot, we couldn't go out.

3. The book is very expensive, so I can't buy it.

-> Because the book is very expensive, I can't buy it.

4. It is very noisy, so I can't write anything.

-> Because it's very noisy, I can't write anything.

5. The room is very dark, so I can see nothing.

-> Because the room is very dark, I can see nothing.

6. She wasn't on time for the party, so she couldn't enter the room.

-> Because she wasn't on time for the party, she couldn't enter the room.

7. He smoked a lot, so he died of lung cancer.

-> Because he smoked a lot, he died of lung cancer.

8. She doesn't know Chinese, so she can't work here.

-> Because she doesn't know Chinese, she can't work here.

9. She is still young, so we can't accept her.

-> Because she is still young, we can't accept her.

10. She didn't find another job, so she was unemployed.

-> Because she didn't find another job, she was unemployed.

11. They didn't study hard, so they failed the important examination.

-> Because they didn't study hard, they failed the important examination.

12. We didn't agree with him, so he left the room without a word.

-> Because we didn't agree with him, he left the room without a word.

13. His disease was an injection, so he was in an isolated room.

-> Because his disease was an injection, he was in an isolated room.

14. He was trained very hard, so he could be a professional player.

-> Because he was trained very hard, he could be a professional player.

15. The coffee is very strong, so I can't drink it.

-> The coffee is very strong, I can't drink it.

16. Water of the river is polluted, so we can't use it for daily life.

-> Because the water of the river is polluted, we can't use it for daily life.

17. The earthquake happened at night, so we couldn't escape from the house.

-> Because the earthquake happened at night, we couldn't escape from the house.

18. The meat is overcooked, so we don't eat it.

-> Because the meat is overcooked, we don't eat it.

19. He didn't wear a warm coat, so he had a bad cold.

-> Because he didn't wear a warm coat, he had a bad cold.

20. It snowed heavily, so we couldn't go on a picnic.

-> Because it snowed heavily, we couldn't go on a picnic.

Nếu bạn muốn chuyển các câu trong Ex5 sang dạng câu dùng với "since" hoặc "as" thì chỉ cần thay "because" trong các câu mình vừa chuyển thành một trong hai từ này là được nhé!

Chúc bạn học tốt!

1) Biểu thức này là P hả?

ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a\ne1\end{matrix}\right.\)

P = \(\dfrac{\sqrt{a^3}-1}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{\sqrt{a^3}+1}{\sqrt{a}\left(\sqrt{a}+1\right)}+\left(\dfrac{a-1}{\sqrt{a}}\right).\left(\dfrac{\left(\sqrt{a}+1\right)^2+\left(\sqrt{a}-1\right)^2}{a-1}\right)\)

= \(\dfrac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)}+\dfrac{a+2\sqrt{a}+1+a-2\sqrt{a}+1}{\sqrt{a}}\)= \(\dfrac{a+\sqrt{a}+1-\left(a-\sqrt{a}+1\right)+2a+2}{\sqrt{a}}\)

= \(\dfrac{a+\sqrt{a}+1-a+\sqrt{a}-1+2a+2}{\sqrt{a}}\)

= \(\dfrac{2a+2\sqrt{a}+2}{\sqrt{a}}\)

2) Để P = 7 với a ∈ ĐKXĐ

⇒ \(\dfrac{2a+2\sqrt{a}+2}{\sqrt{a}}\) = 7

⇔ 2a + 2√a+2 = 7√a

⇔ 2a - 5√a + 2 = 0

⇔ \(\left[{}\begin{matrix}a=2\\a=\dfrac{1}{2}\end{matrix}\right.\)( thoả mãn ĐKXĐ)

Vậy...

3) Để P > 6 với a ∈ ĐKXĐ

⇒ \(\dfrac{2a+2\sqrt{a}+2}{\sqrt{a}}\) >6

⇔ \(\dfrac{2a+2\sqrt{a}+2}{\sqrt{a}}\) - 6 > 0

⇔ \(\dfrac{2a+2\sqrt{a}-6\sqrt{a}+2}{\sqrt{a}}>0\)

Mà √a > 0 với ∀a ∈ ĐKXĐ

⇒ 2a - 4√a + 2 >0

⇔ 2(√a - 1)² > 0

Do 2(√a - 1)² ≥ 0 với ∀a ∈ ĐKXĐ

Nên để 2(√a - 1)² > 0 ⇔ 2(√a - 1)² ≠ 0

⇔ a ≠ 1

Đối chiếu ĐKXĐ ta được: \(\left\{{}\begin{matrix}a>0\\a\ne1\end{matrix}\right.\)

Vậy để P > 6 thì a ∈ ĐKXĐ

a) DKXD: \(\left\{{}\begin{matrix}a>0\\a\ne1\end{matrix}\right.\)

P=\(\left(\dfrac{a-1}{2\sqrt{a}}\right)^2.\left(\dfrac{\left(\sqrt{a}-1\right)^2-\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\\ =\dfrac{\left(a-1\right)^2}{4a}.\left(\dfrac{\left(\sqrt{a}-1-\sqrt{a}-1\right)\left(\sqrt{a}-1+\sqrt{a}+1\right)}{a-1}\right)\)

     = \(\dfrac{a-1}{4a}.\dfrac{-2.2\sqrt{a}}{1}\)

     = \(\dfrac{1-a}{\sqrt{a}}\)

b) P<0 với a ∈ DKXD

=> \(\dfrac{1-a}{\sqrt{a}}< 0\)

mà √a > 0 với ∀a ∈ DKXD

=> 1-a < 0

<=> a>1 ( thoả mãn DKXD)

Vậy để P<0 thì a>1.

c) Để P = 2 với a ∈ DKXD

=> \(\dfrac{1-a}{\sqrt{a}}=2\)

<=> 1-a = 2√a

<=> a + 2√a -1 = 0

<=> \(\left[{}\begin{matrix}\sqrt{a}=-1+\sqrt{2}\\\sqrt{a}=-1-\sqrt{2}\left(loại\right)\end{matrix}\right.\)

<=> a = \(\sqrt{\sqrt{2}-1}\)(thoả mãn DKXD)

Vậy để P =2 thì a = \(\sqrt{\sqrt{2}-1}\)

1. They speak English, Chinese, and Tamil in Malaysia.

English, Chinese, and Tamil are spoken in Malaysia.

2. Women usually wear the ao dai on special occasions.

The ao dai is usually worn by women on special occasions.

3. They sell jeans all over the world.

Jeans are sold all over the world.

4. They grow rice in tropical countries.

Rice is grown in tropical countries.

5. Mr. Parker grows maize on the farm.

Maize is grown on the farm by Mr. Parker.

6. Both teenagers and adults widely read the Kien Thuc Ngay Nay.

The Kien Thuc Ngay Nay is widely read by both teenagers and adults.

7. They use remote controls to interact with the TV.

Remote controls are used to interact with the TV.

8. All Jewish people celebrate Passover in Israel.

Passover is celebrated in Israel by all Jewish people.

9. We often see a lot of water here.

A lot of water is often seen here.

10. Sleepy drivers often cause accidents.

Accidents are often caused by sleepy drivers.

11. The zookeepers feed the animals twice a day.

The animals are fed by the zookeepers twice a day.

12. He always finishes the exercises on time.

The exercises are always finished on time by him.

13. Hoa spends a lot of money on clothes.

A lot of money is spent on clothes by Hoa.

14. Mr. John keeps a large collection of medals.

A large medal collection is kept by Mr. John.

15. Ronaldo wins the gold ball from Fifa.

The gold ball from Fifa is won by Ronaldo.

16. My mother buys a lot of things at this supermarket.

A lot of things at this supermarket are bought by my mother.

17. The beauty of the city really impressed Maryam.

Maryam was impressed by the beauty of the city.

18. Lan and Maryam visited Ho Chi Minh's Mausoleum in Ha Noi.

Ho Chi Minh's Mausoleum in Ha Noi was visited by Lan and Maryam.

19. Lan took Maryam to Hoan Kiem Lake.

Maryam was taken to Hoan Kiem Lake by Lan.

20. Many university students wore jeans in the 1960s.

Jeans were worn by many university students in the 1960s.

21. Liz took a lot of photos last week.

A lot of photos were taken by Liz last week.

22. Jack cleaned the window last week.

The window was cleaned by Jack last week. 

23. They did the work excellently.

The work was excellently done by them.

24. Earthquakes killed a large number of people in 1995.

A large number of people were killed by Earthquakes in 1995.

25. Did people make jeans two hundred years ago?

Were jeans made two hundred years ago?

26. She cut the cake cleverly.

The cake is cleverly cut by her.

27. Christopher Columbus discovered America.

America was discovered by Christopher Columbus.

28. The teacher gave us a lot of presents.

We were given a lot of presents by the teacher.

29. His parents made him study hard for the exam.

He was made to study hard for the exam by his parents.

30. Poets have mentioned the ao dai in poems.

The ao dai has been mentioned in poems by poets.

31. Some fashion designers have printed lines of poetry on the ao dai.

Lines of poetry on the ao dai have been printed by some fashion designers.

32. Some fashion designers have added the symbols to the ao dai.

The symbols have been added to the ao dai by some fashion designers.

33. They have built two department stores this year. 

Two department stores have been built this year.

34. No one has seen Mary since 3 o'clock.

Mary hasn't been seen since 3 o'clock.

35. Trang has just won the first prize.

The first prize has just been won by Trang.

36. People have used the Internet for education in recent years.

The Internet has been used for education in recent years.

37. Famous engineers have designed the washing machine.

The washing machine has been designed by famous engineers.

38. They have just built a new bridge here.

A new bridge has just been built here.

39. The clothing store has just introduced a new style of jeans.

A new style of jeans has just been introduced by the clothing store.

40. The fashion designers have just made a new style of jeans.

A new style of jeans has just been made by fashion designers.

41. You must do this work right away.

This work must be done right away.

42. They will build a new station here.

A new station will be built here.

43. I think he should decorate his room again.

I think his room should be decorated again.

44. You should send this letter before Saturday.

This letter should be sent before Saturday.

45. They have to finish the report today.

The report has to be finished today.

46. We might improve all the schools in the city.

All the schools in the city might be improved.

47. They are going to build a new school in this district.

A new school is going to build in this district.

48. Scientists should stop experiments on animals 

Experiments on animals should be stopped.

49. Nobody can deny the benefits of the internet in our life.

The benefits of the internet can't be denied in our life.

50. Mr. Pike is going to give Mary and Tom some new books.

Mary and Tom are going to be given some new books by Mr. Pike.

51. They will produce five million bottles of champagne next year.

Five million of champagne will be produced next year.

52 Minh must do this exercise carefully.

This exercise must be carefully done by Minh.

53. People can solve the problem easily.

The problem can be easily solved.

54. Nobody can unlock that computer.

That computer can't be unlocked.

1. He's a skillful worker.

He works skillfully.

2. Mrs. Nga speaks English well.

Mrs. Nga is a good English speaker.

3. He's a good English teacher.

He teaches English well.

4. She runs very slowly.

She is a slow runner.

5. My mother cooks very well.

My mother is a good cook/ chef.

6. Betty swims very fast.

Betty is a fast swimmer.

7. Betty designed fashions very cleverly.

Betty is a clever designer.

8. He is always a careful student.

He studies carefully.

9. My Tam is an excellent singer.

My Tam sings excellently.

10. He collects stamps carefully.

He is a careful stamps collector.

11. They work hard.

They are hard-working people.

12. He plays football very well.

He is a good footballer.

13. She studies excellently.

She is an excellent student.

14. My sister is a good cook.

My sister cooks well.

15. They swam very skillfully.

They were skillful swimmers.

16. He actively participated in the game.

He was an active participant in the game.

17. Mary works hard as a student.

Mary is a hard worker as a student.

18. My father drives carefully.

My father is a careful driver.

19. He cycles quite slowly.

He is a slow cyclist.

20. That girl performs attractively.

That girl is an attractive performance.