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\(S=\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}=1-\frac{1}{a+1}+1-\frac{1}{b+1}+1-\frac{1}{c+1}\)

  \(=3-\left(\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\right)\)

\(\frac{1}{a+1}+\frac{9}{16}\left(a+1\right)\ge2\sqrt{\frac{1}{\left(a+1\right)}\cdot\frac{9}{16}\left(a+1\right)}=2\cdot\frac{3}{4}=\frac{3}{2}\)

Tương tự \(\frac{1}{b+1}+\frac{9}{16}\left(b+1\right)\ge\frac{3}{2}\) ; \(\frac{1}{c+1}+\frac{9}{16}\left(c+1\right)\ge\frac{3}{2}\)

=> \(\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}+\frac{9}{16}\left(a+b+c+3\right)\ge\frac{9}{2}\)

=> \(\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}+\frac{9}{4}\ge\frac{9}{2}\Leftrightarrow\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\ge\frac{9}{4}\)

\(\Rightarrow S=3-\left(\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\right)\le3-\frac{9}{4}=\frac{3}{4}\)

Vậy MAX S= 3/4 . Dấu '' = '' xảy ra khi \(\frac{1}{a+1}=\frac{9}{16}\left(a+1\right);\frac{1}{b+1}=\frac{9}{16}\left(b+1\right);\frac{1}{c+1}=\frac{9}{16}\left(c+1\right)\)

                                                          a + b +c = 1 

=> a = b =c =1/3 

Bài này nữa nè bn

Gone are the days when people used to spend all their lives in the same city and the tour was a word for rich people only. Now, with the technological advancements, cheaper flight, and ever increasing awareness towards other states and countries, the world has become a smaller place. Having travelled since childhood, I can definitely say that the tourism industry is changing fast and this is attracting a lot more travellers each year. This essay delves into the reasons behind increasing travellers and benefits of travelling.

Firstly, people want to get refreshed quite often due to their increasing workload and they have easy access to information they want. These are the two main reasons people travel more frequently than ever before. It is evident that busier workdays and the hectic lifestyle can easily drain one out. People have started to work more and earn more as compared to earlier days. Also, with the wave of information that the internet has brought, everyone is better informed about the world outside their office or home. These things have acted as precursors to the increase in the number of people who opt travelling as a holiday get away.

Second, tourism is taken very seriously in several countries now. Countries like Australia and France have travel & tourism as an important part of their economy. Tourism contributes to around 30% of the national GDP for Dubai. Thus, people have started picking up careers in the realm of tourism, as travel bloggers, trip organisers, etc. I myself have met people who travel for a living and love doing so. These factors have also led to accrual in the travelling population.

I believe travelling exposes us to different people and their traditions, outside or even within a country. India itself is a collection of myriad customs, flavours and languages. Visiting places one has never been to and meeting people with different beliefs broadens our perspectives. Introduction to different cultures catalyses respect towards the mutual differences. It helps us understand people in a new light, which can be very helpful to alleviate tensions during political or cultural conflicts.

In a nutshell, I would say that travelling is equivalent to education. It can bring people closer to each other despite their differences, which is very important in today’s global world.

It is believed that the travelling rate of people today is higher than ever. The following essay will discuss some of the factors which affect the situation and several advantages of the activity for the traveller.

There are various reasons why the travelling activities have increased significantly in the past recent years. Firstly, a lot of people travel intensively due to the existence of the low-cost airlines. It is a fact that budget airline companies such as Air Asia or Tiger Air are providing an affordable and economic ticket, therefore, people from a different range of income could purchase it. Secondly, many companies have increased their export and import activities due to the globalisation. As a result, their employees have to do excessive business trips to other regions or other continents. Thirdly, as business competition gets tougher each day, the stress level of the workers has risen. Consequently, the number of people who travel for leisure activities has grown rapidly in the past few years.

It is undeniable that travelling activities bring a lot of benefits for the travellers themselves. As people travel to another country, they would have the chance to learn a new culture. For example, many westerners have visited China, since they were attracted to see the unique culture of the ancient China civilisation such as the Great Wall of China or the Terracotta Army. Travelling also helps people in releasing their stress. It is obvious that people who live in big cities are stressed with their tight schedule and by taking some trips to the countryside; it will help them in loosen the tense.

In conclusion, it is true that travelling activities have increased rapidly in the past recent time, and people are travelling for various kinds of purposes. Some people are taking the trips for business activities, while others are for holiday. Travelling is also a positive activity since people could get a lot of benefits from doing the activity.

Using"in oder(not) to" or "so as(not)to"

He got up early this morning. He wasn't late for work.

-> He got up early this morning so as not to be late for work.

Ejda has to wear boots. Her feet won't get wet.

-> Ejda has to wear boots so as not to get wet.

I go to the library. I want to read books.

-> I go to the library so as to read books.

Minh studies very hard. He wants to pass the entrance exam to Le Hong Phong school.

-> Minh studies very hard so as to pass the entrance exam to Le Hong Phong school.

People use first-aid. They want to ease the victim's pain and anxiety.

-> People use first-aid in order to ease the victim's pain and anxiety.

He is going to take risks.He want to be a winner.

-> He is going to take risks so as to be a winner.

Jed sometimes takes a pill.She wants to go to sleep

-> Jed sometimes takes a pill in order to go to sleep.

Using"in oder(not) to" or "so as(not)to"

He got up early this morning.He wasn't late for work.

-> He got up early this morning so as not to be late for work.

Ejda has to wear boots. Her feet won't get wet.

-> Ejda has to wear boots so as not to get wet.

I go to the library. I want to read books.

-> I go to the library so as to read books.

Minh studies very hard. He wants to pass the entrance exam to Le Hong Phong school.

-> Minh studies very hard in order to pass the entrance exam to Le Hong Phong school.

People use first-aid. They want to ease the victim's pain and anxiety.

-> People use first-aid in order to ease the victim's pain and anxiety.

He is going to take risks. He want to be a winner.

-> He is going to take risks in order to be a winner.

Jed sometimes takes a pill. She wants to go to sleep

-> Jed sometimes takes a pill in order to go to sleep.

1.Joe Smile went to prison because he (steal) had stolen a lot of money.

2.Helen went to bed after she (watch) had watched her favorite TV programm.

Topic 1 : How do you usually do to keep your school clean ?

- Littering the prescribed places

- Do not paint graffiti on the wall

- Classroom sanitation

- Plant trees, water the trees

- Urinate in the prescribed places

- Educating people to keep school hygiene

⇒ Keeping school clean is very important because it helps us: healthy, comfortable, have a green-clean-beautiful school.

Topic 2 : Do you like living in the city or in the countryside ? Why ?

- I like living in the country.

- Country folk are friendly

- Life in coutryside is safe

- The air is fresh, the food is fresh and cheap

- There are a lot of interesting and funny activities: flying kites, riding horse, herding buffaloes, picking fruit, swimming in the rivers, collecting honey from beehives, etc.

- There was so much space ⇒ run around the fields and shout out loud without disturbing anybody

Topic 3 : What do you usually do to relax after study hard ?

- Hanging out with best friends

Topic 4 : What job do you want to become ? How do you prepare your future job ?

* Future job: An English teacher.

* Preparation:

- Hard to learn English when you was a child

- Learn by heart words from English songs or movies

- Studying English yourself is very important ( confident, have more strength, remember better, enhance cognitive abilities, creative, etc)

- Learn from the experience of other people

- Communicate with foreigner

- Create a English environment ( use Note paper)

In my opinion, customs and traditions are very important. Like other families, we have our own customs and traditions. Firstly, there's a tradition in our family of getting together on the first day of Tet. Everyone has tobe there throughout the day. We share every thing with my family members. Secondly, we have the custom of doing morning exercise at 5 a.m together. We always get up early and follow this customs. Thanks to doing morning exercise, we have good health. Thirdly, we visit the pagoda on the first day of every lunar month. This custom is that we have to buy fruit or incense for the pagoda each year. This year, we also prepared five-coloured sticky rice and worshipped Buddha. We all enjoy these customs and traditions because they provide our family with a sense of belonging.