Fill each of the numbered blanks in the following passage. Use only ONE word in each space. The first one has been done for you.

        Most people enjoy going (0) abroad for their holidays, and having the opportunity to (1) ____________ in an interesting city or a seaside (2) ______________. If you speak foreign language, you can make new friends, (3) ______________ take home some interesting souvenirs as presents. But before you can (4) ______________ that, you have to reach your destination, and that is often a problem!

        If you fly, then you may find that your flight has been (5) _______________. Journeys by train can also be difficult (6) _________________ trains are often crowded in the summer, and you might have to (7) _______________ a seat in advance. Whichever way you travel, you can have problems with your luggage, and it is often difficult to find good accommodation. Apart (8) ______________ this, you might not be able to afford the fare!

Find and correct the mistakes in the following sentences.

1. Where is the ruler that I left it on the desk?

2. She is good in English.

3. The people which luggage was lost had to wait a long time.

4. Although Mary was ill, but she went to school.

5. Carol can’t swim today. She is having\f a cold.

6. In the end there was the war between the two countries.

7. As soon as we’ll be ready, we’ll phone you.

8. That was a very strange question for answering

Tìm tất cả các giá trị thực của tham số m để hàm số \(y=\sqrt{x-m}+\sqrt{2x-m-1}\) xác định trên (0: +\(\infty\))

Áp dụng bất đẳng thức Cauchy để chứng minh các bất đẳng thức sau đây với a,b,c là các số thực dương

a) \(\left(ab+c^2\right)\left(bc+a^2\right)\left(ca+b^2\right)\ge abc\left(a+b\right)\left(b+c\right)\left(c+a\right)\)

b) \(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge\frac{a+b}{b+c}+\frac{b+c}{a+b}+1\)

Cho a + b + c = 1 và a,b,c là các số thực dương. CMR: \(\left(ab+c^2\right)\left(bc+a^2\right)\left(ca+b^2\right)\ge abc\left(a+b\right)\left(b+c\right)\left(c+a\right)\)

Cho a + b + c = 1 và a,b,c là các số thực dương. CMR: \(\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ca}{b+ca}}\le\frac{3}{2}\)

Tìm các số nguyên không âm x,y,z,t để biểu thức x² + y² + 2z² + t² đạt giá trị nhỏ nhất, biết rằng: x² - y² + t² = 21 và x² + 3y² + 4z² = 101