11 c)

\(a^2+2\ge2\sqrt{a^2+1}\Leftrightarrow a^2+1-2\sqrt{a^2+1}+1\ge0\Leftrightarrow\left(\sqrt{a^2+1}-1\right)^2\ge0\) (luôn đúng)

12 a)  Có a+b+c=1\(\Rightarrow\) (1-a)(1-b)(1-c)= (b+c)(a+c)(a+b) (*)

áp dụng BĐT cô-si: \(\left(b+c\right)\left(a+c\right)\left(a+b\right)\ge2\sqrt{bc}2\sqrt{ac}2\sqrt{ab}=8\sqrt{\left(abc\right)2}=8abc\) ( luôn đúng với mọi a,b,c ko âm ) 

b)  áp dụng BĐT cô-si: \(c\left(a+b\right)\le\dfrac{\left(a+b+c\right)^2}{4}=\dfrac{1}{4}\)

Tương tự: \(a\left(b+c\right)\le\dfrac{1}{4};b\left(c+a\right)\le\dfrac{1}{4}\)

\(\Rightarrow abc\left(a+b\right)\left(b+c\right)\left(c+a\right)\le\dfrac{1}{4}\dfrac{1}{4}\dfrac{1}{4}=\dfrac{1}{64}\)

13 b) \(\left(a+b\right)\left(ab+1\right)\ge2\sqrt{ab}.2\sqrt{ab}=4ab\)

Dấu = xảy ra khi a=b=1

Câu 106: 

a: Xét ΔABC có 

P là trung điểm của AB

N là trung điểm của AC

Do đó: PN là đường trung bình của ΔABC

Suy ra: PN//BC

hay PN//HM; QN//HM

Xét tứ giác QNMH có QN//HM

nên QNMH là hình thang

mà \(\widehat{QHM}=90^0\)

nên QNMH là hình thang vuông

b: Ta có: ΔAHC vuông tại H

mà HN là đường trung tuyến ứng với cạnh huyền AC

nên \(HN=\dfrac{AC}{2}\left(1\right)\)

Xét ΔABC có

M là trung điểm của BC

P là trung điểm của AB

Do đó: MP là đường trung bình của ΔABC

Suy ra: MP//AC và \(MP=\dfrac{AC}{2}\left(2\right)\)

Từ (1) và (2) suy ra MP=HN

Xét tứ giác MNPH có PN//HM

nên MNPH là hình thang

mà MP=HN

nên MNPH là hình thang cân

câu đầu tiên đây em nhé, k đúng cho chị nhaa

There are several heritage and splendid sights in Vietnam. Especially, Da Nang is one of the most popular place for both Vietnamese and foreign tourist. Da Nang includes sea, Son Tra island, mountain and beautiful landscape. There are a lot of interesting places such as: Asia entertainment park, Ba Na hill, Hoi An ancient town, My Khe beach, museum of art as well as famous bridges. The city is well known for its fresh atmosphere, friendly people and security. The weather is glorious all the year and it brings this city many delicacies from sea and perfect living condition for people, specifically the elder. Visiting Da Nang, I am really impressed by Ba Na hill containing longest cable car from land to the top of the mountain. It is an unforgettable experience for visitors to observe breathtaking sight and picturesque scene. Beside, the beaches have long golden sand, deep blue sea in addition huge bunches of fresh coconut. Tourist has a chance to relax, enjoy the peace and nature, play aqua sport. Moreover, the city has many big bridges : Dragon bridge, Quay bridge and a large outdoor entertainment named Asia park. Additionally, there are a lot of delicious typical dishes such as: Quang noodle, xeo cake, pork pan-cake and others. Da Nang is preserved for its natural beauty; therefore, there is an increasing number of tourists come here. Consequently, it leads to polluted environment, natural damage and other social problem. However, the security of the city is good that there is no street robbery. Hence, Da Nang is voted to be one of the most worth-living cities in Vietnam. In the future, I hope Da Nang will develop and become more popular over the world.

K nha!

There are several heritage and splendid sights in Vietnam. Especially, Da Nang is one of the most popular place for both Vietnamese and foreign tourist. Da Nang includes sea, Son Tra island, mountain and beautiful landscape. There are a lot of interesting places such as: Asia entertainment park, Ba Na hill, Hoi An ancient town, My Khe beach, museum of art as well as famous bridges. The city is well known for its fresh atmosphere, friendly people and security. The weather is glorious all the year and it brings this city many delicacies from sea and perfect living condition for people, specifically the elder. Visiting Da Nang, I am really impressed by Ba Na hill containing longest cable car from land to the top of the mountain. It is an unforgettable experience for visitors to observe breathtaking sight and picturesque scene. Beside, the beaches have long golden sand, deep blue sea in addition huge bunches of fresh coconut. Tourist has a chance to relax, enjoy the peace and nature, play aqua sport. Moreover, the city has many big bridges : Dragon bridge, Quay bridge and a large outdoor entertainment named Asia park. Additionally, there are a lot of delicious typical dishes such as: Quang noodle, xeo cake, pork pan-cake and others. Da Nang is preserved for its natural beauty; therefore, there is an increasing number of tourists come here. Consequently, it leads to polluted environment, natural damage and other social problem. However, the security of the city is good that there is no street robbery. Hence, Da Nang is voted to be one of the most worth-living cities in Vietnam. In the future, I hope Da Nang will develop and become more popular over the world.

K nha!

Bài 1 : 

In Vietnam, there are sixty-four provinces, each with a different name, sometimes associated with the traditions of the province, sometimes called by province characteriss. And there is a very special city, not only because of its beauty, its poe beauty, not only by its cultural traditions, but because of its name, Ho Chi Minh City, The name of the great leader of Vietnam, so that when it comes to Ho Chi Minh City, people will feel something very warm, very dear, even if never arrived.

Ho Chi Minh City is one of the two largest economic, social and cultural centers in Vietnam, with Hanoi capital, Ho Chi Minh City is often associated with a bustling atmosphere the flower of the metropolis. Ho Chi Minh City, formerly known as Saigon, is a centrally-governed city, which is also the city with the largest population size and urbanization rate in the country, Ho Chi Minh City. It is one of the largest cities in the country, with an area of ​​approximately 2,095.06 square kilometers consisting of nineteen counties and five districts.
Ho Chi Minh City is first known as the largest economic and polial center of the country. This is reflected in the GDP structure and its contribution to the overall development of the country, which accounts for about twenty percent of the GDP structure of the country. In Ho Chi Minh City there are many large industrial centers, with many types of economic and service development. On the other hand, Ho Chi Minh City is located in the transshipment area between the big regions of the country, namely the South West and the South East. Therefore, Ho Chi Minh City has good conditions for commodity exchange and development cooperation. economics between regions. Also because of the great development of this city that has attracted a lot of labor here, they came from all over the place
domain of the country.
Ho Chi Minh City is the country with the highest population size and density. According to the statiss of the population, the population of Ho Chi Minh City in 2011 reached 7,521,138 people. Meanwhile, if you include people who do not register to stay may be worth up to ten million. This population density creates conditions for the city to have abundant human resources and conditions for the development of economic sectors. But the reverse side of it is not without, the overcrowding leads to population explosion, unemployment, underemployment, and difficulties in population management and job creation, not to mention the emergence of social evils, environmental pollution.
In terms of geographical location, Ho Chi Minh City is one of the cities in the South East, also the city plays the core role, the main force in the South East. Because it is located in the southern part of the country, the weather in Ho Chi Minh City is hot all year round. During the hot and sunny days, the weather is very cool and favorable for the development of industrial crops. This is also the region with the least natural calamities in the country. Ho Chi Minh City is accreted by the fertile Mekong River, creating a large Mekong Delta region that is conducive to the development of agricultural production. So Ho Chi Minh City is the leading city in terms of average food per capita, not only provide food for people in the country but also for export. High economic returns.

It is the geographical location and benefits that this location brings to Ho Chi Minh City. Also in terms of historical tradition, this is also a city with a tradition in the fight against foreign invaders. Whenever there are foreign invaders, Ho Chi Minh City is always one of the three leading cities in the struggling country, together with Hanoi and Hue City. In parular, in the struggle against American imperialism, Ho Chi Minh City, then known as Saigon, was the center of major American military and military forces. That is why this is the focal point of the struggles, which witness all the ups and downs of Vietnamese history. Congress in 1976 decided to rename Saigon into Ho Chi Minh City, city named Uncle.

Thus, Ho Chi Minh City is one of the two largest centers of economics, polis, culture and education of Vietnam, together with the capital of Hanoi, Ho Chi Minh City has been developing. Rapid economic development, contributing greatly to the development of the country of Vietnam. Not only is the center of economic development, Ho Chi Minh City is also a city rich in historical traditions as well as a long-standing cultural tradition.

Câu 2

\((1) MnO_2 + 4HCl \to MnCl_2 + Cl_2 + 2H_2O\\ (2) Cl_2 + H_2 \xrightarrow{as} 2HCl\\ (3) 3Cl_2 + 2Fe \xrightarrow{t^o} 2FeCl_3\\ (4) 2FeCl_3 + Fe \to 3FeCl_2\\ (5) 2NaOH + Cl_2 \to NaCl + NaClO + H_2O\)

\((1) 4Al + 3O_2 \xrightarrow{t^o} 2Al_2O_3\\ (2) 2Fe + 3Cl_2 \xrightarrow{t^o} 2FeCl_3\\ (3) C + O_2 \xrightarrow{t^o} CO_2\\ (4) 2KMnO_4 \xrightarrow{t^o} K_2MnO_4 + MnO_2 + O_2\\ (5) 4P + 5O_2 \xrightarrow{t^o} 2P_2O_5\\ (6) 2KClO_3 \xrightarrow{t^o} 2KCl + 3O_2\\ (7) Fe + H_2SO_4 \to FeSO_4 + H_2\\ (8) Cu + 2H_2SO_4 \to CuSO_4 + SO_2 + 2H_2O\\ (9) 2Fe + 6H_2SO_4 \to Fe_2(SO_4)_3 + 3SO_2 + 6H_2O\\ (10) 2Al + 6H_2SO_4 \to Al_2(SO_4)_3 + 3SO_2 + 6H_2O\)

Bài 2: 

a: Ta có: ΔABC cân tại A

mà AH là đường cao

nên AH là tia phân giác của góc BAC

b: Xét ΔAMH vuông tại M và ΔANH vuông tại N có

AH chung

\(\widehat{MAH}=\widehat{NAH}\)

Do đó: ΔAMH=ΔANH

Suy ra: AM=AN

hay ΔAMN cân tại A

c: Xét ΔABC có AM/AB=AN/AC

nên MN//BC

d: \(AH^2-AN^2=HN^2\)

\(BH^2-BM^2=MH^2\)

mà HN=MH

nên \(AH^2-AN^2=BH^2-BM^2\)

hay \(AH^2+BM^2=BH^2+AN^2\)

ta có Cu ko tác dụng được vs H2SO4 

-> 2,24 lít khí H2 đc tạo ra là do phản ứng HH của Fe va H2SO4 

\(PTHH:\) \(Fe+H_2SO_4->FeSO_4+H2\)

n H2 = 2,24 :22,4=0,1 mol 

n H2 = n Fe =0,1 mol 

m Fe = 0,1.56=5,6 g 

m Cu = 10-5,6=4,4 g 

vậy giá trị của x là 4,4 g

26 

PTHH : \(Zn+2HCl->ZnCl_2+H_2\)

n Zn = 6,5:65=0,1 mol

n ZnCl2 = n Zn =0,1 mol

m ZnCl2 = 0,1.(65+35,5.2)=13,6 g

ta có Cu ko tác dụng được vs H2SO4 

-> 2,24 lít khí H2 đc tạo ra là do phản ứng HH của Fe va H2SO4 

n H2 = 2,24 :22,4=0,1 mol 

n H2 = n Fe =0,1 mol 

m Fe = 0,1.56=5,6 g 

m Cu = 10-5,6=4,4 g 

vậy giá trị của x là 4,4 g