a) Theo giả thiết, ta có: \(x+y=1\Rightarrow\left(x+y\right)^3=1^3\Leftrightarrow x^3+y^3+3xy\left(x+y\right)=1\Leftrightarrow x^3+y^3+3xy=1\)

b) Theo giả thiết, ta có: \(x+y=5\Rightarrow\left(x+y\right)^2=5^2\Leftrightarrow x^2+2xy+y^2=25\Leftrightarrow x^2+y^2=19\)

Lại có: \(x+y=5\Rightarrow\left(x+y\right)^3=5^3\Leftrightarrow x^3+y^3+3xy\left(x+y\right)=125\Leftrightarrow x^3+y^3=80\)

Ta có: 

- \(x^2+y^2=19\Rightarrow\left(x^2+y^2\right)^2=19^2\Leftrightarrow x^4+2x^2y^2+y^4=361\Leftrightarrow x^4+y^4=343\)

- \(x^5+y^5=\left(x+y\right)\left(x^4+y^4\right)-xy\left(x^3+y^3\right)=5.343-3.80=1475\)

c) Theo giả thiết, ta có: \(x+y=3\Rightarrow\left(x+y\right)^2=3^2\Leftrightarrow x^2+2xy+y^2=9\Leftrightarrow2xy=4\Leftrightarrow xy=2\)

Do đó: \(x^3+y^3=\left(x+y\right)\left(x^2+y^2\right)-xy\left(x+y\right)=3.5-2.3=9\)

1) He wondered what he should do.

2) They don't know how they should eat healthily.

3) Harry asked if he should turn off his mobile phone at hight.

\(\left(-\dfrac{1}{2}a^3b^4c^5\right):\dfrac{3}{2}a^2bc^5=\left(-\dfrac{1}{2}:\dfrac{3}{2}\right)\left(a^3:a^2\right)\left(b^4:b\right)\left(c^5:c^5\right)=-\dfrac{1}{3}ab^3\)

He (addicted to / is addicted to) playing video games. He (spends / has spent / spending) 10 hours (to play / playing) games every day. Playing games can have (negative / negative) effect (on / to) his eyes.

I think we can rely (at / in / on) (him / he / his). He is (enough smart / too smart / such smart / smart enough) (helping / to help) us. He promised (helping / to help) us.

Lenka admitted (stealing / stole / steal) my money. She was so (embarrassing / embarrassed). 

You used to be a doctor, _________? (weren’t you / haven’t you / didn’t you)

________ the terrible storm, a lot of houses were destroyed last night. (Because / Because of / Although / Despite)

1. If she doesn't practice more, she will find it hard to pass the exam.

2. If it doesn't rain soon, millions of pounds worth of crops will be lost.

3. If you don't get a visa, you can't visit the US.

4. If we don't leave now, we will miss the train.

5. If he doesn't phone immediately, he won't get any information.

6. If we recycle, we will save natural resources.

7. If you aren't careful, you will fall over the rock.

8. If he buys recycled product, he can do a part to save the environment.

9. If we go on wasting water, there will be a shortage of fresh water.

10. If you litter the place around you, it will be a junk yard.

11. If you don't reduce the use of energy, you'll pay more for it.

12. If you don't practice your English regularly, your English doesn't improve.

13. If he doesn't take the map with him, he'll lose his way in the forest.

14. If she practices English every day, she will speak it perfectly.

How prepared are you for the future? You are studying to obtain qualifications for your chosen career, but what about getting the business skills necessary to make your career a success? How do you gain the advantage that will get you your dream job? Perhaps you even have the ambition to set up a business yourself?

Every year since 2007, when the Young Enterprise Programme began, hundreds of thousands of young people have gained a head start while they are still at school by taking part in a Young Enterprise programme. There, they have gained key business skills and knowledge, either through a series of workshops or through starting and running their own real company. At Young Enterprise, we believe that it is important for learning to be exciting, fun and hands-on, which is __________ our programmes are run on the principle of learning by doing.

To participate in the programme, your first step is to consult your school. Your school will need to become a centre if it has __________ yet done so. It can register as one of these by contacting the nearest Young Enterprise office. Once it has registered as a centre, you can get started!

3. If you ask him for advice, you will find a way out.

4. Mr Binh has recycled rubbish for four years.

5. Mr Hoang plays golf more skillful than Mr Long.

6. Since there was a hurricane last night, I was without electric power.

a) \(G=2016^2-2015^2+2014^2-2013^2+2012^2-2011^2+...+2^2-1^2\)

\(=\left(2016-2015\right)\left(2016+2015\right)+\left(2014-2013\right)\left(2014+2013\right)+\left(2012-2011\right)\left(2012+2011\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=2016+2015+2014+2013+2012+2011+...+2+1\) (có \(\left(2016-1\right)+1=2016\) (số hạng))

\(=\left(2016+1\right)+\left(2015+2\right)+\left(2014+3\right)+\left(2013+4\right)+\left(2012+5\right)+\left(2011+6\right)+...+\left(1009+1008\right)\) (có \(2016:2=1008\) (cặp))

\(=2017+2017+2017+2017+2017+2017+...+2017\) 

\(=1008.2017\)

\(=2033136\)

b) \(M-N+50\)

\(=\left(99^2+97^2+95^2+...+3^2+1^2\right)-\left(98^2+96^2+94^2+...+4^2+2^2\right)+50\)

\(=\left(99^2-98^2\right)+\left(97^2-96^2\right)+\left(95^2-94^2\right)+...+\left(5^2-4^2\right)+\left(3^2-2^2\right)+1+50\)

\(=\left(99-98\right)\left(99+98\right)+\left(97-96\right)\left(97+96\right)+\left(95-94\right)\left(95+94\right)+...+\left(5-4\right)\left(5+4\right)+\left(3-2\right)\left(3+2\right)+51\)

\(=\left(99+98+97+96+95+94+...+5+4+3+2\right)+51\)

Đặt \(A=99+98+97+96+95+94+...+5+4+3+2\) ta có:

\(A=99+98+97+96+95+94+...+5+4+3+2\) (có \(\left(99-2\right)+1=98\) (số hạng))

\(=\left(99+2\right)+\left(98+3\right)+\left(97+4\right)+\left(96+5\right)+\left(95+6\right)+\left(94+7\right)+...+\left(51+50\right)\) (có \(98:2=49\) (cặp))

\(=101+101+101+101+101+101+...+101\)

\(=101.49\)

\(=4949\)

Khi đó: \(M-N+50=A+51=4949+51=5000\)

29. A

30. C

31. A

32. C

Trinh Cong Son is considered to be a great music => musician in Viet Nam

His bother can => could phay the piano when he was two and now he practices it every day