Số đó là 9999

c)( 3X+9)(11-X) = 0

3x +9 =0 => x=-3

11-x =0  =>x = 11

1/ a) \(4x^2+4x+5>0\)

<=> \(\left(4x^2+4x+1\right)+4>0\)
<=> \(\left(2x+1\right)^2+4>0\) (bất đẳng thức đúng với mọi x)

b) \(a^2+ab+b^2\)≥ 0

<=> \(2a^2+2ab+2b^2\) ≥ 0

<=> \(\left(a^2+2ab+b^2\right)+a^2+b^2\) ≥ 0

<=> \(\left(a+b\right)^2+a^2+b^{2^{ }}\) ≥ 0 (bất đẳng thức đúng với mọi a,b)

Dấu "=" xảy ra khi a + b = a = b = 0 hay a = b = 0.

2/

[Mình vẽ hình tượng trưng thôi chứ không đúng đâu nhé]

Xét tam giác ABD và tam giác ACE có

Góc A chung

AB = AC (Tam giác ABC cân tại A)

Góc ABD = góc ACE (=góc B/2 = góc C/2)

Suy ra: Tam giác ABD = tam giác ACE (g.c.g)

=> AE = AD (2 cạnh tương ứng)

=> Tam giác AED cân tại A

△ABC cân tại A

=> góc B = (180^o - góc A)/2 (1)

△AED cân tại A (cmt)

=> góc AED = (180^o - góc A)/2 (2)

Từ (1) và (2) => góc B = góc AED

=> ED //BC

=> Tứ giác BEDC là hình thang

mà góc B = góc C (Tam giác ABC cân tại A)

=> BEDC là hình thang cân.

3/ \(1+x+x^2+x^3=y^3\)

Ta nhận thấy: 1 + x + x² = \(\left(x+\dfrac{1}{2}\right)^{2^{ }}+\dfrac{3}{4}>0\) với mọi x

nên x³ < 1 + x + x² + x³ hay x³ < y³ (1)

Xét hiệu (x+2)³ - y³ = (x+2)³ - (1+x+x²+x³) = 5x² + 11x + 7

= \(5\left(x+\dfrac{11}{10}\right)^{2^{ }}+\dfrac{19}{20}>0\) nên (x+2)³ > y³ (2)

Từ (1) và (2) => x³ < y³ < (x+2)³

=> y³ = (x+1)³ (vì x,y là số nguyên)

hay 1 + x + x² + x³ = (x+1)³

<=> x² + x = 0 <=> x(x+1) = 0 <=> x = 0 hoặc x = -1

* Với x = -1 thì y = 1 + (-1) + (-1)² + (-1)³ = 0

* Với x = 0 thì y = 1 + 0 + 0² + 0³ = 1

Vậy Các số nguyên (x;y) cần tìm là (-1;0); (0;1).

4/ \(\left(x^2-\dfrac{25}{4}\right)^2=10x+1\)

<=> \(x^4-\dfrac{25}{2}x^2+\dfrac{625}{16}=10x+1\)

<=> \(x^4-\dfrac{25}{2}x^2-10x+\dfrac{609}{16}=0\)

<=> \(\left(x^4-\dfrac{7}{2}x^3\right)+\left(\dfrac{7}{2}x^3-\dfrac{49}{4}x^2\right)-\left(\dfrac{1}{4}x^2-\dfrac{7}{8}x\right)-\left(\dfrac{87}{8}x+\dfrac{609}{16}\right)=0\)

<=> \(\left(x-\dfrac{7}{2}\right)\left(x^3+\dfrac{7}{2}x^2-\dfrac{1}{4}x-\dfrac{87}{8}\right)=0\)

<=> \(\left(x-\dfrac{7}{2}\right)\left[\left(x^3-\dfrac{3}{2}x^2\right)+\left(5x^2-\dfrac{15}{2}x\right)+\left(\dfrac{29}{4}x-\dfrac{87}{8}\right)\right]=0\)

<=> \(\left(x-\dfrac{7}{2}\right)\left(x-\dfrac{3}{2}\right)\left(x^2+5x+\dfrac{29}{4}\right)=0\)

<=> \(x-\dfrac{7}{2}=0\) hoặc \(x-\dfrac{3}{2}=0\) (vì \(x^2+5x+\dfrac{29}{4}\)≠ 0)

<=> x = 3.5 hoặc x = 1.5.

Tìm số nguyên x biết:

a) (x-28) : (-12) = -5

b) (x+15) : (-28) = 8

c) (x+30) : (-45) = -14

9:9+9 

=1+9

=10

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions.

        Lighthouses are towers with strong lights that help mariners plot their position, inform them that land is near, and warn them of dangerous rocks and reefs. They are placed at prominent points on the coast and on islands, reefs, and sandbars.

       Every lighthouse has a distinctive pattern of light known as its characteristic. There are five basic characteristics: fixed, flashing, occulting, group flashing, and group occulting. A fixed signal is a steady beam. A flashing signal has periods of darkness longer than periods of light, while an occulting signal’s periods of light are longer. A group-flashing light gives off two or more flashes at regular intervals, and a group - occulting signal consists of a fixed light with two or more periods of darkness at regular intervals. Some lighthouses use lights of different colors as well, and today, most lighthouses are also equipped with radio beacons. The three types of apparatus used to produce the signals are the catoptric, in which metal is used to reflect the light; the dioptric, in which glass is used; and the catadioptric, in which both glass and metal are used.

        In the daytime, lighthouses can usually be identified by their structure alone. The most typical structure is a tower tapering at the top, but some, such as the Bastion Lighthouse on the Saint Lawrence River, are shaped like pyramids, and others, such as the Race Rock light, look like wooden houses sitting on high platforms. Still others, such as The American Shoal lighthouse off the Florida Coast, are skeletal towers of steel. Where lighthouses might be contused in daylight, they can be distinguished by day- marker patterns - designed of checks and stripes painted in vivid colors on lighthouse walls.

       In the past, the job of lighthouse keeper was lonely and difficult if somewhat romantic. Lighthouse keepers put in hours of tedious work maintaining the lights. Today, lighthouses are almost entirely automated with humans supplying only occasional maintenance. Because of improvements in navigational technology, the importance of lighthouses has diminished. There are only about 340 functioning lighthouses in existence in the United States today, compared to about 1,500 in 1900, and there are only about 1,400 functioning lighthouses outside the United States. Some decommissioned lighthouses have been preserved as historical monument.

According to the passage, a catoptric apparatus is one that uses_________.

A. lights of various colors

B. metal

C. glass

D. a radio beacon

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks.

        Everybody has heard about the Internet, do you know what an “intranet” is? It is this: just as the Internet connects people around the world, intranets connect people within a single company. In fact,

intranets make use of the same software programs as the Internet to (34)_____computers and people. This means that you do not have to buy a lot of additional programs to set up an intranet service. If your intranet is working properly, it can link together a huge amount of (35)______which is stored in different

places in the company. In this way, people can get the information they need, regardless (36)_____where it comes from. A company intranet can, of course, be used for unimportant information like office memos  or canteen menus. But an intranet should provide important information which people need to make decision about new products, costs and so on. The intranet is (37)_______to share their information with other people. Unfortunately, many departments don’t want to share their specialist knowledge with others. Another problem (38)____often occurs is that top managers like to use the intranet to “communicate down” rather than to “communicate across”. That is, they use the intranet to give orders, not to share information between themselves and others working in the same organization.

Điền vào ô 38.

A. that

B. when

C. where

D. whose