Lời giải:

$x^2-6x+3=4y^2$

$\Leftrightarrow (x^2-6x+9)-6=4y^2$

$\Leftrightarrow (x-3)^2-6=4y^2$
$\Leftrightarrow 6=(x-3)^2-4y^2=(x-3)^2-(2y)^2=(x-3-2y)(x-3+2y)$

Ta thấy: $x-3-2y+(x-3+2y)=2(x-3)$ chẵn nên $x-3-2y, x-3+2y$ có cùng tính chẵn lẻ.

Mà tích $(x-3-2y)(x-3+2y)=6=1.6=6.1=2.3=3.2$ đều là các thừa số khác tính chẵn lẻ

$\Rightarrow$ không tồn tại $x,y$ nguyên thỏa mãn đề.

\(x^2\) - 6\(x\) + 3 = 4y²; \(x\); y \(\in\) Z  ⇒ \(x^2\) - 6\(x\) + 3 ⋮ 4

Nếu \(x\) = 2k ⇒ (2k)² - 6.2k + 3 ⋮ 4 ⇒ 4k² - 12k + 3 ⋮ 4 ⇒ 3 ⋮ 4(loại)(*)

Nếu \(x\) = 2k + 1 ⇒ (2k + 1)² - 6(2k + 1) + 3 ⋮ 4  

⇒ 4k²+ 4k +1 - 12k - 6 + 3 ⋮ 4 ⇒ 4k² - 8k - 2 ⋮ 4 ⇒ 2 ⋮ 4(loại)(**)

Từ (*);(**) ta có không tồn tại \(x;y\) thỏa mãn đề bài. 

x2nho

41 to

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1. If the work is finished by lunchtime, you can go home.

à Get__________home when the work is finished by lunchtime __________________________________________________________________

2. You haven’t done your work, have you?

à It’s about________time you did your work_______________________________________________________________

3. The fourth time he asked her to marry him, she accepted.

à Only on his ________fourth proposal did she accept him_____________________________________________________________

4. He said that he had won as a result of good luck.

à He attributed___________ his success to good luck_________________________________________________________

5. That reminds me of the time I climbed to the top of Mount Fuji.                

à That takes me_________ back to the time I climbed to the top of Mount Fuji__________________________________________________________

6. People rumour that he is rich but stingy.

à What______people rumour is that he is rich but stingy _____________________________________________________________________

7. Such a ridiculous proposal isn’t worth serious consideration.

à There is____________ no point in considering such a ridiculous proposal seriously.

_____________________________________________________________

8. Just thinking about his face at that moment makes me laugh.

à The very_____ thought of his face at that moment makes me laugh____________________________________________________________________

9.We cannot see animals in a vast area after the forest fire.                  

à There is an_________ absence of animal in vast area after the forest fire______________________________________________________________

10.The staff hated Frank’s new policies so intensely that they went on strike.

à So intense _________was the hatred for Frank's new policies that they went on strike ______________________________________________________________

1 solved => been solved

2 think => thinking

3 seem => seems

4 them => themselves 

5 spent => took

6 first place => the first place

7 believed in => believed that

8 by the chance => by chance

9 project => projected

10 reach at => reach

1 known

2 some

3 no

4 means

5 other

6 in

7 many

8 wish

9 celebrations

10 while

1. What does the passage mainly discuss?

A. States's rights versus federal rights.

B. The participation of state governments in railroad, canal, and turnpike construction.

C. The roles of state and federal governments in the economy of the nineteenthcentury.

D. Regulatory activity by state governments.

2. The word “effect” in bold in paragraph 1 is closest in meaning to __________.

A. value                                 B. argument               C. influence               D. restraint

3. All of the following are mentioned in the passage as areas that involved statevernments in the nineteenth century EXCEPT _________.

A. mining                              B. banking                             C. manufacturing      D. higher education

4. The word “distinct” in bold in paragraph 1 is closest in meaning to_________.

A. separate                B. innovative                        C. alarming                           D. provocative

5. It can be inferred from the first paragraph that in the nineteenth century canals and railroads were ______.

A. built with money that came from the federal government

B. much more expensive to build than they had been previously

C. built predominantly in the western part of the country

D. sometimes built in part by state companies

6. The regulatory activities of state governments included all of the following EXCEPT_______.

A. licensing of retail merchants                             B. inspecting materials used in turnpike maintenance

C. imposing limits on price-fixing                         D. control of lumber

7. The word “setting” in bold in paragraph 2 is closest in meaning to _________.

A. discussing            B. analyzing                          C. establishing          D. avoiding

8. The word “ends” in bold in paragraph 3 is closest in meaning to ________.

A. benefits                            B. decisions                          C. services                 D. goals

9. According to the passage, which of the following is true of the Homestead Act of 1862?

A. It made it increasingly possible for settlers to obtain land in the West.

B. It was a law first passed by state governments in the West.

C. It increased the money supply in the West.

D. It established tariffs in a number of regions.

10. Which of the following activities was the responsibility of the federal government in the nineteenth century?

A.Control of the manufacture of gunpowder.

B. Determining the conditions under which individuals worked.

C. Regulation of the supply of money.

D. Inspection of new homes built on western lands.