9.

1. Between 1442 and 1779, eighty-one exams were held by the Le dynasty.

2. Many people think that children live in the rural area happier and more free than those in the city.

10. 

1. The 28^th Sea Games will be held in Singapore this week.

2. It takes us two hours to do the household chores every day.

3. My younger brother paint more creative than I do.

4. Though Mark didn't like the CD you have recommended me, he bought it all the same.

Điều kiện: \(x,y\ne0\)

\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{5}\)

\(\Leftrightarrow\dfrac{5x}{5xy}+\dfrac{5y}{5xy}=\dfrac{xy}{5xy}\)

\(\Rightarrow5x+5y-xy=0\)

\(\Leftrightarrow\left(5x-xy\right)-\left(25-5y\right)=-25\)

\(\Leftrightarrow x\left(5-y\right)-5\left(5-y\right)=-25\)

\(\Leftrightarrow\left(x-5\right)\left(5-y\right)=-25\)

Vì \(-25=-1.25=-5.5=-25.1=25.\left(-1\right)=5.\left(-5\right)=1.\left(-25\right)\) nên ta có 6 trường hợp.

Trường hợp 1: \(x-5=-1\Leftrightarrow x=4\) (nhận)

Trường hợp 2: \(x-5=-5\Leftrightarrow x=0\) (loại)

Trường hợp 3: \(x-5=-25\Leftrightarrow x=-20\) (nhận)

Trường hợp 4: \(x-5=25\Leftrightarrow x=30\) (nhận)

Trường hợp 5: \(x-5=5\Leftrightarrow x=10\) (nhận)

Trường hợp 6: \(x-5=1\Leftrightarrow x=6\) (nhận)

Vậy \(x\in\left\{-20;4;6;10;30\right\}.\)

41. The police have warned tourists to look_______ for pickpockets in the town centre.
a. out b. up c. down d. forward
42. I wouldn't_______ of going to a party unless I hadn't been invited to.
a. intend b. dream c. rely d. depend
43. If you want to be healthy; you should cut_______ on your smoking.
a. up b. down c. out d. through
44. Their aim is to_______ up a new political party.
a. strike b. stand c. set d. show
45. He was busy when I phoned but I hung_______ until he was free.
a. back b. off c. to d. on
46. I'm not sure how old he is but he must be _______ for 70.
a. going by b. getting up c. getting on d. going off
47. I absolutely_______ with everything that has been said.
a. agree b. accept c. admit d. approve
48. The man who lives opposite us sometimes comes _______ for a cup for coffee.
a. on b. over c. off d. to
49. The butcher cut some steak, _______ it up and handed it to me.
a. closed b. wound c. strung d. wrapped
50. In order to _______ with his studies he worked though the summer.
a. take b. catch on c. catch up d. take up
51. A god friend will stand _______ you when you're having trouble.
a. by b. out c. against d. in
52. The meeting had to be put_______ until a later date.
a. away b. on c. off d. up
53. The teachers at the school went_______ with flu one after the other.
a. out b. down c. off d. under
54. The smell was so bad that it completely_______ us off our food.
a. set b. took c. got d. put
55. We expected him at eight but the finally_______ at midnight.
a. came to b. turned out c. turned in d. came off
56. The hall was very crowded with over fifty people_______ into it.
a. pushed b. packed c. stuck d. stuffed
57. He took the trouble to write_______ the complete list for us.
a. on b. through c. off d. our
58. He had to go to the bank to_______ some money for his holiday.
a. pay up b. pay back c. draw out d. draw in
59. A new study group has been _______ by the United Nations
a. set up b. set on c. put up d. put on
60. David always_______ over to my house after he had done his homework.
a. passed b. gone c. went d. came

1. The carrots appeared to be bad.

2. I didn’t have the courage to tell him what I really thought.

4. He didn't think he would win.

5. I was astonished to find the stranger knew my name.

Vì \(\Delta ABC=\Delta EOM\) (giả thiết)

\(\Rightarrow\left\{{}\begin{matrix}AC=EM=2cm\\\widehat{M}=\widehat{C}=40^o\end{matrix}\right.\) (tương ứng)

1. He asked if he had to do it.

2. The mother asked her daugher where her daugher had been.

3. She asked what they were doing.

4. She asked me how I knew that.

5. She asked me where her umbrella was.

21. d. fill in
22. b. cut
23. a. along
24. c. from
25. d. off
26. b. on
27. a. off
28. c. by
29. d. of
30. b. face
31. c. back
32. a. down
33. d. get over
34. b. round
35. c. off
36. d. applied
37. a. down with
38. b. across
39. c. off
40. d. on

Theo giả thiết, ta có: \(3m-2n=5\Rightarrow\left(3m-2n\right)^2=5^2\Leftrightarrow9m^2-12mn+4n^2=25\Leftrightarrow9m^2+4n^2=13\)

Lại có: \(9m^2+4n^2=13\Rightarrow\left(9m^2+4n^2\right)^2=13^2\Leftrightarrow81m^4+72m^2n^2+16n^4=169\Leftrightarrow81m^4+16n^4=97\)

Vậy: \(C=97.\)

\(\left(2x^2+x-2020\right)^2+4\left(x^2-5x-2021\right)^2=4\left(2x^2+x-2020\right)\left(x^2-5x-2021\right)\)

Đặt \(\left\{{}\begin{matrix}a=2x^2+x-2020\\b=x^2-5x-2021\end{matrix}\right.,\) khi đó phương trình trở thành:

\(a^2+4b^2=4ab\Leftrightarrow a^2-2.a.2b+\left(2b\right)^2=0\Leftrightarrow\left(a-2b\right)^2=0\Leftrightarrow a-2b=0\Leftrightarrow a=2b\)

Với \(a=2b,\) ta có:

\(2x^2+x-2020=2\left(x^2-5x-2021\right)\Leftrightarrow2x^2+x-2020=2x^2-10x-4042\Leftrightarrow11x=-2022\Leftrightarrow x=-\dfrac{2022}{11}\)

Vậy phương trình có tập nghiệm là: \(S=\left\{-\dfrac{2022}{11}\right\}.\)

\(\left(2x+3\right)^3+\left(3x-5\right)^3=\left(5x-2\right)^3-\left(5x-2\right)\left(17x^2+2016x-2063\right)\)

\(\Leftrightarrow\left\{\left(2x+3\right)^3+\left(3x-5\right)^3+3\left(2x+3\right)\left(3x-5\right)\left[\left(2x+3\right)+\left(3x-5\right)\right]\right\}-3\left(2x+3\right)\left(3x-5\right)\left[\left(2x+3\right)+\left(3x-5\right)\right]=\left(5x-2\right)^3-\left(5x-2\right)\left(17x^2+2016x-2063\right)\)

\(\Leftrightarrow\left(2x+3+3x-5\right)^3-3\left(2x+3\right)\left(3x-5\right)\left(2x+3+3x-5\right)=\left(5x-2\right)^3-\left(5x-2\right)\left(17x^2+2016x-2063\right)\)

\(\Leftrightarrow\left(5x-2\right)^3-3\left(5x-2\right)\left(2x+3\right)\left(3x-5\right)=\left(5x-2\right)^3-\left(5x-2\right)\left(17x^2+2016x-2063\right)\)

\(\Leftrightarrow3\left(5x-2\right)\left(2x+3\right)\left(3x-5\right)-\left(5x-2\right)\left(17x^2+2016x-2063\right)=0\)

\(\Leftrightarrow\left(5x-2\right)\left[3\left(2x+3\right)\left(3x-5\right)-\left(17x^2+2016x-2063\right)\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-2=0\\3\left(2x+3\right)\left(3x-5\right)-\left(17x^2+2016x-2063\right)=0\end{matrix}\right.\)

Trường hợp 1: \(5x-2=0\Leftrightarrow x=\dfrac{2}{5}\)

Trường hợp 2: \(3\left(2x+3\right)\left(3x-5\right)-\left(17x^2+2016x-2063\right)=0\)

\(\Leftrightarrow3\left(6x^2-10x+9x-15\right)-\left(17x^2+2016x-2063\right)=0\)

\(\Leftrightarrow18x^2-30x+27x-45-17x^2-2016x+2063=0\)

\(\Leftrightarrow x^2-2019x+2018=0\)

\(\Leftrightarrow\left(x^2-2018x\right)-\left(x-2018\right)=0\)

\(\Leftrightarrow x\left(x-2018\right)-\left(x-2018\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2018\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2018=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2018\end{matrix}\right.\)

Vậy phương trình có tập nghiệm là: \(S=\left\{\dfrac{2}{5};1;2018\right\}.\)