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Ta có : \( \left|a\right|+\left|b\right|\ge\left|a+b\right|\)

\(\Leftrightarrow\left(\left|a\right|+\left|b\right|\right)^2\ge\left(\left|a+b\right|\right)^2\)

\(\Leftrightarrow\left(\left|a\right|\right)^2+2\left|ab\right|+\left(\left|b\right|\right)^2\ge\left(\left|a\right|\right)^2+2ab+\left(\left|b\right|\right)^2\)

\(\Leftrightarrow\left|ab\right|\ge ab\) ( Luôn đúng )

Dấu ""=" xảy ra \(\Leftrightarrow a\cdot b\ge0\)

Với mọi a,b \(\in\)Q, ta luôn có 

a \(\le|a|\) và -a \(\le|a|\)

b\(\le|b|\)và - b \(\le|b|\)

suy ra a+b \(\le|a|\)+\(|b|\) và -a-b \(\le|a|\)+\(|b|\)

vậy \(|a+b|\)\(\le|a|\)+\(|b|\)

dấu "=" khi và chỉ khi ab \(\ge\)0

IX Read the passage and decide whether the statement are True (T) or False (F).

Machu Picchu

            Machu Picchu is an ancient city in Peru. The construction of the city started in 1450. The city covers about 13 square kilometers. For centuries, the city was buried in the jungle and was not discovered until 1911. Today, Machu Picchu is one of the most famous tourist attractions in all parts of South America.

            The Great Wall of China is the longest man-made Structure ever built. Much of what exists of the wall is much older and go back to around 200 B.C. The wall is about 11 meters high. The main part of the wall stretches for about 3,400 kilometers.

Decide if the statements are True (T) or False (F).

      1.   Machu Picchu is a modern city in Peru.                                                       F

      2.   People began to build the city in 1450.                                                        T

      3.   The city was built on the area of thirty square kilometers.                            F

      4.   People found the city buried in the jungle in 1911.                                       T

      5.   The city attracts many tourists from South America.                                   F

      6.   The Great Wall of China was constructed by man.                                      T

      7.   The Great Wall is the longest wall in the world.                                          T

      8.   Many parts of the wall were built around 200 B.C.                                       T

      9.   The height of the wall is about 11 meters.                                                    T

      10. The main part of the wall is about 3,200 kilometers long.                             F

X Read the passage and answer the questions given below.

            Indonesia is an island nation in Southeast Asia. Its official name is the Republic of Indonesia. It is a member country of the Association of South East Asian Nations (ASEAN). The country’s total area is 1,904,443 sq km. Vietnam and othercountries in Southeast Asia, Indonesia enjoys tropical climate. The rupiah is the official monetary unit of Indonesia, consisting of 100 sen.

            The capital of Indonesia is Jakarta and it is also the largest city in the country. Other big cities are Bandung, Surabaya, Medan, Palembang... The population in 2004 was about 238,500,000. Indonesia is the world’s fourth most populous country after China, India, and the United States. Islam, which is over eighty per cent of the population prace, is the country’s official religion. In addition, there are other religions such as Protestantism, Catholicism, Buddhism, Hinduism...

            The national language is Bahasa Indonesia, which is a modified form of Malay.Besides, about 300 other languages and dialects are spoken. English is increasingly used as the language of business.

Answer the questions:

      1.   Where is Indonesia?

      Indonesia is in Southeast Asia

      2.   What is Indonesia’s area?

      The country’s total area is 1,904,443 sq km

      3.   What is Indonesia’s official monetary?

        The rupiah is the official monetary unit of Indonesia

      4.   What is the biggest city in Indonesia?

 Jakarta is the largest city in the country

      5.   How many languages are spoken in Indonesia?

    About 300 other languages and dialects are spoken

ĐẶt \(A=3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^{200}}\)

\(A=3\left(\text{​​}\text{​​}1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{200}}\right)\)

Đặt \(B=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{200}}\)

\(2B=2+\frac{1}{1}+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{199}}\)

2B-B = \(2-\frac{1}{2^{200}}\)

B= \(2-\frac{1}{2^{200}}\)

A= \(6-\frac{3}{2^{200}}\)

 mik chỉ dịch đc thôi

Sinh viên Mỹ có nhiều kỳ nghỉ hơn sinh viên Việt Nam.

-> Sinh viên Việt Nam....................................

Vietnamese students have fewer vacations than American students

1. She made her son wash the windows before he could go outside to play with his friends. ( make sb do st; modal verb + V- inf)

2.She promised to give the book back to me. ( promise to do)

3.She let her children stay up very late. ( let sb do st. Ex: let's go)

4.It is important to start the meeting on time. ( adj to do)

5.There are too many people here for me to talk to all of them.

6.We often prace speaking English wit our friends.( prace doing)

7.Ann is interested in teaching children.( prep doing)

8.I finished reading the book and went to bed. ( finish doing )

9.My sister suggested revising the leson in the early morning. ( suggest doing )

10.It is dangerous to play soccer on the streets. ( adj to do)

11.I used to drink lot of milk when I was young. ( used to do)

12.Mary can swim across a river. ( modal verb do)

13.He enjoys collecting stamps.( enjoy doing)

14.I'd to go somewhere different for a change.( would to do )

15.My teacher encouraged me to take.the course ( encourage to do)

\(B=\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2017}\)

\(-5B=\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2018}\)

\(-5B-B=\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2018}-\)\(\left[\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2017}\right]\)

 \(-6B=\left(-5\right)^0-\left(-5\right)^{2018}\)

\(B=\left(5^{2018}-1\right):6\)