No one present noticed anything strange.

A.                The people who were there didn’t notice anything strange.

B.                 The people who were there didn’t notice anything usual.

C.                 The people were there didn’t notice anything strange.

D.                The people who were there didn’t notice something strange.

52.     Jane refused to attend his birthday party, which made him feel sad.

A.                Jane’s refusal to attend his birthday party made him feel sad.

B.                 He felt sad not to be able to attend his birthday party.

C.                 Jane made him sad despite her refusal to attend his birthday party.

D.                Jane refused to attend his birthday party because it made him feel sad.

53.     The plants may develop differently. They grow on that island.

A.                The plants which grows on that island may develop differently.

B.                 The plants which grow on that island may develop differently.

C.                 The plants  grow on that island may develop differently.

D.                The plants which grow that island may develop differently.

54.     John Smith is a farmer. I bought his land.

A.                John Smith, whose land I bought, is a farmer.

B.                 John Smith, who is a farmer, whose land I bought.

C.                 John Smith, whom I bought his land, is a farmer.

D.                John Smith, a farmer, bought his land.

55.     The first man who was interviewed was entirely unsuitable.

A.                The first man interviewing was entirely unsuitable.

B.                 The first man to interview was entirely unsuitable.

C.                 The first man was interviewed was entirely unsuitable.

D.                The first man to be interviewed was entirely unsuitable.

56.     Astronomy is the study of planets and stars. It is one of the world’s oldest sciences

A.                Astronomy which is the study of planets and stars is one of the world’s oldest sciences

B.                 Astronomy, who is the study of planets and stars, is one of the world’s oldest sciences

C.                 Astronomy is the study of planets and stars which are one of the world’s oldest sciences

D.                Astronomy,  the study of planets and stars,  is one of the world’s oldest sciences

57.     Our solar system is in a galaxy. It is called the Milky Way.

A.                Our solar system is in a galaxy where is called the Milky Way.

B.                 Our solar system is in a galaxy called the Milky Way.

C.                 Our solar system is in a galaxy, that is called the Milky Way.

D.                Our solar system is in a galaxy calling the Milky Way.

58.     I saw men, women, cats and dogs. They moved round and round.

A.                I saw men, women, cats and dogs that moved round and round.

B.                 I saw men, women, cats and dogs which moved round and round.

C.                 I saw men, women, cats and dogs moved round and round.

D.                I saw men, women, cats and dogs when moved round and round.

59.      One evening, he and the writer went to a restaurant. They had a wonderful meal in it.

A.                One evening, he and the writer went to a restaurant which they had a wonderful meal.

B.                 One evening, he and the writer went to a restaurant where they had a wonderful meal in.

C.                 One evening, he and the writer went to a restaurant where they had a wonderful meal.

D.                One evening, he and the writer went to a restaurant they had a wonderful meal.

60.      A number of suggestions were made at the meeting, but most of them were not very practical.

A.                A number of suggestions were made at the meeting,  most of them were not very practical

B.                 A number of suggestions were made at the meeting, most of which were not very practical

C.                 A number of suggestions were made at the meeting, but most of which were not very practical

D.                Most of the suggestions which were made at the meeting were not very practical.

61. ________ in 1937, the Golden Gate Bridge spans the channel at the entrance to San Francisco Bay.

      A. Completed                  B. Having completed               C. Completing                D. To be completed

62. After seeing the movie Centennial, __________.

A. the book made many people want to read it                 B. many people want to read the book

C. the reading of the book interested many people           D. the book was read by many people

63. _____ of the shop, my friend came in.
   A. Coming out                     B. On coming out                C. When coming out         D. As I came out 
64. _________ two hours over lunch, they left the restaurant,.

   A. Spending                         B. Having spent                   C. After spend                  D. Spent

65. I notice the lorry _________ down the hill.

   A. having come                    B. coming                             C. to come                         D. came

66. _____________, I decided to stop trading with them.

   A. Despite of the fact that they were the biggest dealer

   B. Though being the biggest dealer

   C. Being the biggest dealer 

   D. Even though they were the biggest dealers

67. She told a very funny story, ____________everyone to burst into a laugh.

   A. allowing                          B. making                             C. taking                           D. causing

68. I wasn't properly dressed for the party and felt ____________about my appearance.

   A. embarrass                        B. embarrassment                 C. embarrassing                 D. embarrassed

69. Young people _____________to succeed in life should work hard.

   A. who wanting                   B. want                                C. wanting                        D. wanted

70. _______________is known to be good for digestion.

   A. Eating yoghurt                B. Having eaten yoghurt      C. Yoghurt eaten              D. Yoghurts

71.   ________ over the exam results,she  rushed home to tell her family the good news.

   A. Excited                            B. Excitement                      C. To excite                       D. Exciting

72. Are there any household chores for________ men are better _______ than women ?

   A. that/suit                           B. whose/suited                   C. which/suited                 D. which/suit

73. Can you please tell me some information _______ to the job ?

   A. relating                            B. that relate                        C. that are relating            D. that related

74. The truck _______ crashed into the back of a bus scattering glass everywhere.

   A. it was loading with empty bottles                                B. loaded with empty bottles

   C. which loading with empty bottles                                D. loading with empty bottles

75. None of the people __________to the party can come.

   A. invite                               B. invited                             C. inviting                         D. to invite

76. ____________ the noise and pollution in the city, the Browns move to the countryside.

   A. Be tired of                       B. Being tired of                 C. Tired of                        D. Were tired of

77. the author / released /earned / last year / the book / a lot of money.

   A. Released last year, the book earned the author a lot of money.   

   B. Released last year, the author earned the book a lot of money.

   C. The author released the book last year a lot of money earned.    

   D. The released book last year earned the author a lot of money.

78. Do you know any restaurant……………. ?

         A. have a really good meal                                          B. where we can have a really good meal

         C. has a really good meal                                            D. that we can have a really good meal 

79. The secretaries were the only people……………………..

                                               A. to get a pay rise                                                           B. getting a pay rise           

        C. who to get a pay rise                                               D. to whom get a pay rise.

80. The reason………….. was that her mother fell seriously ill.

        A. where she didn’t come                                            B. when she didn’t come          

        C. she didn’t come                                                       D. for which she didn’t come

#\(\text{ }Cụt\)

#\(yGLinh\)

  No one present noticed anything strange.

A.                The people who were there didn’t notice anything strange.

B.                 The people who were there didn’t notice anything usual.

C.                 The people were there didn’t notice anything strange.

D.                The people who were there didn’t notice something strange.

52.     Jane refused to attend his birthday party, which made him feel sad.

A.                Jane’s refusal to attend his birthday party made him feel sad.

B.                 He felt sad not to be able to attend his birthday party.

C.                 Jane made him sad despite her refusal to attend his birthday party.

D.                Jane refused to attend his birthday party because it made him feel sad.

53.     The plants may develop differently. They grow on that island.

A.                The plants which grows on that island may develop differently.

B.                 The plants which grow on that island may develop differently.

C.                 The plants  grow on that island may develop differently.

D.                The plants which grow that island may develop differently.

54.     John Smith is a farmer. I bought his land.

A.                John Smith, whose land I bought, is a farmer.

B.                 John Smith, who is a farmer, whose land I bought.

C.                 John Smith, whom I bought his land, is a farmer.

D.                John Smith, a farmer, bought his land.

55.     The first man who was interviewed was entirely unsuitable.

A.                The first man interviewing was entirely unsuitable.

B.                 The first man to interview was entirely unsuitable.

C.                 The first man was interviewed was entirely unsuitable.

D.                The first man to be interviewed was entirely unsuitable.

56.     Astronomy is the study of planets and stars. It is one of the world’s oldest sciences

A.                Astronomy which is the study of planets and stars is one of the world’s oldest sciences

B.                 Astronomy, who is the study of planets and stars, is one of the world’s oldest sciences

C.                 Astronomy is the study of planets and stars which are one of the world’s oldest sciences

D.                Astronomy,  the study of planets and stars,  is one of the world’s oldest sciences

57.     Our solar system is in a galaxy. It is called the Milky Way.

A.                Our solar system is in a galaxy where is called the Milky Way.

B.                 Our solar system is in a galaxy called the Milky Way.

C.                 Our solar system is in a galaxy, that is called the Milky Way.

D.                Our solar system is in a galaxy calling the Milky Way.

58.     I saw men, women, cats and dogs. They moved round and round.

A.                I saw men, women, cats and dogs that moved round and round.

B.                 I saw men, women, cats and dogs which moved round and round.

C.                 I saw men, women, cats and dogs moved round and round.

D.                I saw men, women, cats and dogs when moved round and round.

59.      One evening, he and the writer went to a restaurant. They had a wonderful meal in it.

A.                One evening, he and the writer went to a restaurant which they had a wonderful meal.

B.                 One evening, he and the writer went to a restaurant where they had a wonderful meal in.

C.                 One evening, he and the writer went to a restaurant where they had a wonderful meal.

D.                One evening, he and the writer went to a restaurant they had a wonderful meal.

60.      A number of suggestions were made at the meeting, but most of them were not very practical.

A.                A number of suggestions were made at the meeting,  most of them were not very practical

B.                 A number of suggestions were made at the meeting, most of which were not very practical

C.                 A number of suggestions were made at the meeting, but most of which were not very practical

D.                Most of the suggestions which were made at the meeting were not very practical.

61. ________ in 1937, the Golden Gate Bridge spans the channel at the entrance to San Francisco Bay.

      A. Completed                  B. Having completed               C. Completing                D. To be completed

62. After seeing the movie Centennial, __________.

A. the book made many people want to read it                 B. many people want to read the book

C. the reading of the book interested many people           D. the book was read by many people

63. _____ of the shop, my friend came in.
   A. Coming out                     B. On coming out                C. When coming out         D. As I came out 
64. _________ two hours over lunch, they left the restaurant,.

   A. Spending                         B. Having spent                   C. After spend                  D. Spent

65. I notice the lorry _________ down the hill.

   A. having come                    B. coming                             C. to come                         D. came

66. _____________, I decided to stop trading with them.

   A. Despite of the fact that they were the biggest dealer

   B. Though being the biggest dealer

   C. Being the biggest dealer 

   D. Even though they were the biggest dealers

67. She told a very funny story, ____________everyone to burst into a laugh.

   A. allowing                          B. making                             C. taking                           D. causing

68. I wasn't properly dressed for the party and felt ____________about my appearance.

   A. embarrass                        B. embarrassment                 C. embarrassing                 D. embarrassed

69. Young people _____________to succeed in life should work hard.

   A. who wanting                   B. want                                C. wanting                        D. wanted

70. _______________is known to be good for digestion.

   A. Eating yoghurt                B. Having eaten yoghurt      C. Yoghurt eaten              D. Yoghurts

71.   ________ over the exam results,she  rushed home to tell her family the good news.

   A. Excited                            B. Excitement                      C. To excite                       D. Exciting

72. Are there any household chores for________ men are better _______ than women ?

   A. that/suit                           B. whose/suited                   C. which/suited                 D. which/suit

73. Can you please tell me some information _______ to the job ?

   A. relating                            B. that relate                        C. that are relating            D. that related

74. The truck _______ crashed into the back of a bus scattering glass everywhere.

   A. it was loading with empty bottles                                B. loaded with empty bottles

   C. which loading with empty bottles                                D. loading with empty bottles

75. None of the people __________to the party can come.

   A. invite                               B. invited                             C. inviting                         D. to invite

76. ____________ the noise and pollution in the city, the Browns move to the countryside.

   A. Be tired of                       B. Being tired of                 C. Tired of                        D. Were tired of

77. the author / released /earned / last year / the book / a lot of money.

   A. Released last year, the book earned the author a lot of money.   

   B. Released last year, the author earned the book a lot of money.

   C. The author released the book last year a lot of money earned.    

   D. The released book last year earned the author a lot of money.

78. Do you know any restaurant……………. ?

         A. have a really good meal                                          B. where we can have a really good meal

         C. has a really good meal                                            D. that we can have a really good meal 

79. The secretaries were the only people……………………..

                                               A. to get a pay rise                                                           B. getting a pay rise           

        C. who to get a pay rise                                               D. to whom get a pay rise.

80. The reason………….. was that her mother fell seriously ill.

        A. where she didn’t come                                            B. when she didn’t come          

        C. she didn’t come                                                       D. for which she didn’t come

Bài 5

A B C D E y x

\(\widehat{A}+\widehat{D}=180^o\) (Hai góc trong cùng phía bù nhau)

\(\widehat{DAx}=\widehat{BAx}=\dfrac{\widehat{A}}{2}\) (gt)

\(\widehat{ADy}+\widehat{CDy}=\dfrac{\widehat{D}}{2}\) (gt)

\(\Rightarrow\widehat{DAx}+\widehat{ADy}=\dfrac{\widehat{A}}{2}+\dfrac{\widehat{D}}{2}=\dfrac{180^o}{2}=90^o\)

Xét tg ADE có

\(\widehat{AED}=180^o-\left(\widehat{DAx}+\widehat{ADy}\right)=180^o-90^o=90^o\) (Tổng các góc trong của tg bằng 180 độ)

\(\Rightarrow Ax\perp Dy\)

Bài 6:

A B C E D

a/

Ta có

AB//CD => AB//DE

BE//AB (gt)

=> ABED là hình bình hành (Tứ giác có các cặp cạnh đối // với nhau từng đôi một là hbh)

=> AB = DE; AD = BE (Trong hình bình hành các cạnh đối nhau thì bằng nhau)

b/

CD - DE = CE

Mà AB = DE (cmt)

=> CD - AB = CE

c/

Xét tg BCE có

BC+BE>CE (trong tg tổng độ dài 2 cạnh lớn hơn độ dài cạnh còn lại)

Mà CE = CD - DE và DE = AB (cmt) và BE = AD

=> BC+BE = BC + AD>CE = CD - AB

Gọi G là giao điểm của hai đường phân giác Ax và By 

Ta có: \(\widehat{ADG}\) = \(\dfrac{1}{2}\)\(\widehat{ADE}\) ( vì DG là phân giác góc ADE)

           \(\widehat{DAG}\) = \(\dfrac{1}{2}\)\(\widehat{DAB}\)( vì AG là phân giác góc DAB )

     ⇒ \(\widehat{ADG}\) + \(\widehat{DAG}\) = \(\dfrac{1}{2}\)\(\widehat{ADE}\) + \(\dfrac{1}{2}\)\(\widehat{DAB}\) = \(\dfrac{1}{2}\)(\(\widehat{ADE}\) + \(\widehat{DAB}\)) 

           \(\widehat{ADE}\) + \(\widehat{DAB}\) = 180⁰ (vì hai góc là hai góc trong cùng phía)

      ⇒ \(\widehat{ADG}\) + \(\widehat{DAG}\) = \(\dfrac{1}{2}\) \(\times\) 180⁰ = 90⁰

          Xét tam giác ADG có: \(\widehat{GAD}\) + \(\widehat{ADG}\) + \(\widehat{DGA}\) = 180⁰ (tổng ba góc trong 1 tam giác bằng 180⁰)

               ⇒ \(\widehat{DGA}\)  = 180⁰ - 90⁰ = 90⁰

Vậy tam giác ADG vuông tại G ⇒AE \(\perp\) DG (đpcm)

\(x+y=a\left(1\right)\)

\(x-y=b\left(2\right)\)

\(\left(1\right)+\left(2\right)\Rightarrow2x=a+b\Rightarrow x=\dfrac{a+b}{2}\)

\(\left(1\right)\Rightarrow y=a-x\Rightarrow y=a-\dfrac{a+b}{2}\Rightarrow y=\dfrac{a-b}{2}\)

\(xy=\dfrac{\left(a+b\right)}{2}.\dfrac{\left(a-b\right)}{2}=\dfrac{a^2-b^2}{4}\)

\(x^3-y^3=\left(\dfrac{a+b}{2}\right)^3-\left(\dfrac{a-b}{2}\right)^3=\dfrac{\left(a+b\right)^3}{8}-\dfrac{\left(a-b\right)^3}{8}\)

\(=\dfrac{\left(a+b\right)^3-\left(a-b\right)^3}{8}\)

\(=\dfrac{\left(a+b-a+b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]}{8}\)

\(=\dfrac{2b\left[a^2+b^2+2ab+a^2-b^2+a^2+b^2-2ab\right]}{8}\)

\(=\dfrac{b\left[3a^2+b^2+2ab\right]}{4}\)

\(\left\{{}\begin{matrix}x+y=a\\x-y=b\end{matrix}\right.\) tính \(x^3\) - y³ theo \(a\) và \(b\)

⇒ \(\left\{{}\begin{matrix}x+y+x-y=a+b\\x-y=b\end{matrix}\right.\)

⇔ \(\left\{{}\begin{matrix}2x=a+b\\y=x-b\end{matrix}\right.\)

⇔ \(\left\{{}\begin{matrix}x=\left(a+b\right):2\\y=\left(a-b\right):2\end{matrix}\right.\) ⇒ \(xy\) = \(\dfrac{a+b}{2}\)\(\times\)\(\dfrac{a-b}{2}\) = \(\dfrac{a^2-b^2}{4}\)

\(x^{3^{ }}\) - y³ = (\(x\) - y)(\(x^2\) + \(x\)y + y²) = \(\left(x-y\right)\)\(\left(\left[x+y\right]^2-xy\right)\) (1)

Thay \(x-y\) = a; \(x\) + y = b và \(xy\) = \(\dfrac{a^2-b^2}{4}\) vào (1) ta có:

\(x^3\) - y³ = b.(a² - \(\dfrac{a^2-b^2}{4}\)) = b.\(\dfrac{3a^2+b^2}{4}\) = \(\dfrac{3a^2b+b^3}{4}\)

Khối lượng của dầu và nước là :

\(m_d=m_n=\dfrac{1,2}{2}=0,6\left(g\right)\)

Thể tích của dầu là :

\(V_d=\dfrac{m}{D}=\dfrac{0,6}{800}=7,5.10^{-4}\left(m^3\right)\)

Thể tích của nước : 

\(V_n=\dfrac{m}{D}=\dfrac{0,6}{1000}=6.10^{-4}\left(m^3\right)\)

Sự nỗ lực hết mình trong cuộc sống là một khía cạnh quan trọng để chúng ta đạt được thành công và đạt được mục tiêu của mình. Đó là sự cống hiến tuyệt đối và không ngừng nghỉ để đạt được những điều mà chúng ta mong muốn. Ý nghĩa của sự nỗ lực hết mình không chỉ là về việc đạt được thành công mà còn là về quá trình phát triển bản thân và trở thành phiên bản tốt nhất của chính mình. Đầu tiên, sự nỗ lực hết mình giúp chúng ta vượt qua những khó khăn và thách thức trong cuộc sống. Cuộc sống không phải lúc nào cũng suôn sẻ và dễ dàng. Chúng ta thường gặp phải những trở ngại và thử thách mà không thể tránh khỏi. Tuy nhiên, khi chúng ta nỗ lực hết mình, chúng ta có thể vượt qua những khó khăn này và tiến lên phía trước. Sự nỗ lực hết mình giúp chúng ta không bỏ cuộc và không đánh mất hy vọng. Nó truyền động lực và sự kiên nhẫn để chúng ta tiếp tục cố gắng và không ngừng nghỉ. Thứ hai, sự nỗ lực hết mình giúp chúng ta phát triển bản thân và trở thành phiên bản tốt nhất của chính mình. Khi chúng ta đặt mục tiêu và nỗ lực hết mình để đạt được chúng, chúng ta không chỉ đạt được thành công mà còn trở nên mạnh mẽ và tự tin hơn. Quá trình nỗ lực hết mình giúp chúng ta khám phá và phát triển những khả năng tiềm ẩn của bản thân. Chúng ta học cách vượt qua giới hạn và phát triển những kỹ năng mới. Sự nỗ lực hết mình cũng giúp chúng ta rèn luyện sự kiên nhẫn và sự kiên trì, hai yếu tố quan trọng để đạt được thành công trong cuộc sống. Cuối cùng, sự nỗ lực hết mình mang lại cho chúng ta cảm giác tự hào và hạnh phúc. Khi chúng ta đạt được những mục tiêu mà chúng ta đã đặt ra và nhìn lại quá trình chúng ta đã đi qua, chúng ta cảm thấy tự hào về những gì chúng ta đã đạt được. Sự nỗ lực hết mình cũng mang lại cho chúng ta cảm giác hạnh phúc và thỏa mãn vì chúng ta biết rằng chúng ta đã đặt tất cả sức lực và tâm huyết vào những gì chúng ta làm. Trong cuộc sống, sự nỗ lực hết mình là một yếu tố quan trọng để đạt được thành công và đạt được mục tiêu của chúng ta. Nó giúp chúng ta vượt qua khó khăn, phát triển bản thân và mang lại cảm giác tự hào và hạnh phúc. Vì vậy, hãy luôn nỗ lực hết mình và không ngừng nghỉ để đạt được những điều mà chúng ta mong muốn trong cuộc sống.

a, (\(x-2\))² - (2\(x\) + 3)² = 0

     (\(x\) - 2 - 2\(x\) - 3)(\(x\) - 2 + 2\(x\) + 3) = 0

     (-\(x\) - 5)(3\(x\) +1) = 0

      \(\left[{}\begin{matrix}-x-5=0\\3x+1=0\end{matrix}\right.\)

       \(\left[{}\begin{matrix}x=-5\\3x=-1\end{matrix}\right.\)

        \(\left[{}\begin{matrix}x=-5\\x=-\dfrac{1}{3}\end{matrix}\right.\)

Vậy \(x\in\) { -5;- \(\dfrac{1}{3}\)}

b, 9.(2\(x\) + 1)² - 4.(\(x\) + 1)² = 0 

    {3.(2\(x\) + 1) - 2.(\(x\) +1)}{ 3.(2\(x\) +1) + 2.(\(x\) +1)} = 0

    (6\(x\) + 3 - 2\(x\) - 2)(6\(x\) + 3 + 2\(x\) + 2) = 0

      (4\(x\) + 1)(8\(x\) + 5) =0

        \(\left[{}\begin{matrix}4x+1=0\\8x+5=0\end{matrix}\right.\)

          \(\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=-\dfrac{5}{8}\end{matrix}\right.\)

          S = { - \(\dfrac{5}{8}\); \(\dfrac{-1}{4}\)}

d, \(x^2\)(\(x\) + 1) - \(x\) (\(x+1\)) + \(x\)(\(x\) -1) = 0

      \(x\left(x+1\right)\).(\(x\) - 1) + \(x\)(\(x\) -1) = 0

        \(x\)(\(x\) -1)(\(x\) + 1 + 1) = 0

            \(x\left(x-1\right)\left(x+2\right)\) = 0

             \(\left[{}\begin{matrix}x=0\\x-1=0\\x+2=0\end{matrix}\right.\)

               \(\left[{}\begin{matrix}x=0\\x=1\\x=-2\end{matrix}\right.\)

              S = { -2; 0; 1}

a)\(\left(x-2\right)^2-\left(2x+3\right)^2=0\Rightarrow\left(x-2+2x+3\right)\left(x-2-2x-3\right)=0\)

\(\Rightarrow\left(3x+1\right)\left(-x-5\right)=0\Rightarrow\left[{}\begin{matrix}3x+1=0\\-x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=-5\end{matrix}\right.\)

b)\(9\left(2x+1\right)^2-4\left(x+1\right)^2=0\Rightarrow\left[3\left(2x+1\right)+2\left(x+1\right)\right]\left[3\left(2x+1\right)-2\left(x+1\right)\right]=0\)

\(\Rightarrow\left[8x+5\right]\left[4x+1\right]=0\Rightarrow\left[{}\begin{matrix}8x+5=0\\4x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{8}\\x=\dfrac{1}{4}\end{matrix}\right.\)

c)\(x^3-6x^2+9x=0\Rightarrow x\left(x^2-6x+9\right)=0\Rightarrow x\left(x-3\right)^2=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)

d) \(x^2\left(x+1\right)-x\left(x+1\right)+x\left(x-1\right)=0\)

\(\Rightarrow x\left(x+1\right)\left(x^2-1\right)+x\left(x-1\right)=0\)

\(\Rightarrow x\left(x+1\right)\left(x-1\right)\left(x+1\right)+x\left(x-1\right)=0\)

\(\Rightarrow x\left(x-1\right)\left[\left(x+1\right)\left(x+1\right)+1\right]=0\)

\(\Rightarrow x\left(x-1\right)\left[\left(x+1\right)^2+1\right]=0\)

Do \(\left(x+1\right)^2+1>0\)

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

a)x²-6x+9

=x²-2.x.3+3²

=(x-3)²

b)4x²+4x+1

=(2x)²+2.2x.1+1²

=(2x+1)²

c)4x²+12xy+9y²

=(2x)²+2.2x.3y+(3y)²

=(2x+3y)²

d)4x⁴-4x²+4

=(2x²)²-2.2x².2+2²

=(2x²-2)²

a) Ta có:

VT = (x - y)² + 4xy

= x² - 2xy + y² + 4xy

= x² + 2xy + y²

= (x + y)²

= VP

b) Ta có:

(x + y)² = (x - y)² + 4xy

= 5² + 4.3

= 25 + 12

= 37