Giải các phương trình sau:
a. \(\sqrt{25x+75}+2\sqrt{9x+27}=5\sqrt{x+3}+18\)
b. \(\sqrt{4x-8}-14\sqrt{\dfrac{x-2}{49}}=\sqrt{9x-18}+8\)

Giải các phương trình sau:
a. \(\sqrt{25x+75}+3\sqrt{x-2}=2\sqrt{x-2}+\sqrt{9x-18}\)

b. \(\sqrt{\left(2x-1\right)^2}=4\)
c. \(\sqrt{\left(2x+1\right)^2}=3x-5\)

d. \(\sqrt{4x-12}-14\sqrt{\dfrac{x-2}{49}}=\sqrt{9x-18}+8\)

Rút gọn:
\(A=\dfrac{2}{x-1}\sqrt{\dfrac{x^2-2x+1}{4x^2}}\)
\(B=\left(x^2-4\right)\sqrt{\dfrac{9}{x^2-4x+4}}\)

Tính:

\(A=\sqrt{20}-2\sqrt{45}+3\sqrt{18}+\sqrt{72}\)
\(B=4\sqrt{\left(\sqrt{3}-1\right)^2}+2\sqrt{12}+4\sqrt{\dfrac{1}{2}}\)
\(C=\left(3+\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\right)\left(3-\dfrac{3+\sqrt{3}}{1+\sqrt{3}}\right)\)
\(D=\dfrac{1}{2+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\)

Rewrite the following sentences, beginning as shown and keep the meaning stay the same:

1. Would you close the door, please?

® Would you mind ......................................................................................................... ?

2. They didn’t allow us to smoke in here.

® They didn’t let .............................................................................................................

3. My teacher advised buying that book.

- My teacher advised us ..................................................................................................              

4. The thief forced the bank manager to lie on the ground.

- The thief made................................................................................................................

5. He has studied English for six years.

- He began .........................................................................................................................

6. It is necessary to master English.

- Mastering ........................................................................................................................

7. He spent two hours writing the essay.

- It took ..............................................................................................................................

8. He is too young to ride a motorbike.

- He isn’t ...........................................................................................................................

9. The bag was so heavy that she couldn’t carry it upstairs.

- The bag was too .............................................................................................................

10. He expects to hear from her as soon as possible.

- He is looking forward ...................................................................................................

11. It’s not a good idea to travel during the rush hour.

- It’s better to avoid .........................................................................................................

12. Please don’t interrupt me all the time.

- Would you mind                                                                                                            ?

13. I remember someone telling me the news.

- I remember being ...........................................................................................................

14. Are you sure you paid those bills yesterday?

- Do you remember......................................................................................................... ?

15. Don’t forget that you have to do this homework.

- Please remember ...........................................................................................................

16. I think we’ve discussed phrasal verbs enough now.

- Let’s stop ........................................................................................................................

17. The film isn’t very good.

- It’s not worth                                                                                                                   

18. Don’t study if you feel tired.

- There’s no.......................................................................................................................

19. I managed to get a visa but it was difficult.

- I had difficulty................................................................................................................

20. Buying the thing you don’t need is a waste of money.

- It’s a waste of        

Exercise 3. Give the correct form of each verb in brackets to complete the following sentences:

1. I don't really fancy (spend) ______ my whole holiday with your cousins. I'd rather (spend) ______my time with you.

2. We had hoped (finish) ______ the project by the end of the month but we keep (delay) ______ by changes in the plans.

3. You'd better (go) ______ and see the boss and say what you've done. If you put off (explain) ______ it to her, she'll only be more annoyed.

4. No, that's not what I meant (say) ______. How can I make you (understand) ______?

5. Those shirts need (iron) ______, but you don't need (iron) ______ them now.

6. Are we permitted (bring) ______ guests to the ceremony? I'd like (invite) ______ my friend to join us.

7. Children shouldn't be allowed (watch) ______ violent programs on TV. Parents should encourage their children (spend) _____ time (play) _____ outdoors.

8. They couldn’t help (laugh) ______ when they heard the little boy singing a love song.

9. I can’t bear thinking back of that time. I’d rather (treat) ______ equally by all of members in my family.

10. Ann: “Did you accuse Nam of (break) ______ a plate?”

Peter: “Well, I saw him (knock) ______ it off the table with his elbow.”