Vì AH là đường cao nên góc AHB = 90 độ

Ta có : góc B + góc BAH + góc BHA = 180 độ

=> 60 độ + góc BAH + 90 độ = 180 độ

=> góc BAH = 180 độ - 60 độ - 90 độ = 30 độ

Ta có : \(\frac{AB}{3}=\frac{AC}{7}\Rightarrow\frac{AB^2}{9}=\frac{AC^2}{49}\) \(\Rightarrow\frac{\frac{1}{9}}{\frac{1}{AB^2}}=\frac{\frac{1}{49}}{\frac{1}{AC^2}}\)

Mặt khác, ta có \(\frac{1}{AB^2}+\frac{1}{AC^2}=\frac{1}{AH^2}=\frac{1}{42^2}\)

\(\Rightarrow\frac{\frac{1}{9}}{\frac{1}{AB^2}}=\frac{\frac{1}{49}}{\frac{1}{AC^2}}=\frac{\frac{1}{9}+\frac{1}{49}}{\frac{1}{AB^2}+\frac{1}{AC^2}}=\frac{\frac{58}{441}}{\frac{1}{42^2}}=232\)

\(\Rightarrow\begin{cases}AB^2=2088\\AC^2=11368\end{cases}\) \(\Rightarrow\begin{cases}AB=6\sqrt{58}\\AC=14\sqrt{58}\end{cases}\)

Vậy ............................................

Đặt P(x)=x⁴+6x³+7x²- 6x+1

Đặt y=x²-1

=>y²=x⁴-2x²+1

P(x)=x⁴-2x²+1+6x³-6x+9x²

  =(x²-1)²+6x(x²-1)+9x²

Q(y)=y²+6xy+9x²

=(y+3x)²

P(x)=(x²-1+3x)²

Ta có : \(p^2-1=\left(p-1\right)\left(p+1\right)\)

Vì p là số nguyên tố, p > 3 nên p không chia hết cho 3

Xét tích ba số nguyên liên tiếp : (p-1).p.(p+1) . Số này chia hết cho 3 vì một trong ba số ắt tìm được một số chia hết cho 3. Mà p không chia hết cho 3

=> (p-1)(p+1) = p²-1 chia hết cho 3 (1)

Ta chứng minh bài toán phụ : Với mọi số nguyên tố lớn hơn 3 đều viết được dưới dạng \(6m+1\) hoặc \(6m-1\)

Thật vậy , mọi số nguyên đều viết được dưới dạng \(6m\pm1,6m\pm2,6m\pm3\)

Mọi số nguyên tố lớn hơn 3 thì không chia hết cho 2 và 3 nên chúng chỉ có dạng \(6m\pm1\)

Xét với số nguyên tố \(p=6m\pm1\Rightarrow p^2-1=36m^2\pm12m=12m\left(3m\pm1\right)⋮8\) (2)

Từ (1) và (2) suy ra p chia hết cho 3 và 8 , mà (3,8) = 1

=> p chia hết cho 24

2. your / classmate / where / live / does?

=> Where does your classmate live?

3. have / any / doesn't / in / she / friends / Ha Noi

=> She doesn't have any friends in Ha Noi

4. new / has / a / students / of / her / school / lot

=> Her new school has a lot of students

=> Her school has a lot of new students.

1. My brother often goes swimming when it's school (xem lại đề)

=> What does your brother often do when it's school?

2.It is two kilometers from his house to the supermarket.

=> How far is it from his house to the supermarket?

3. My children are going to stay with their grandmother.

=> Who are your children going to stay with?

4. Lan is waiting for her friends near the bus stop

=> Where is Lan waiting for her friends?

5. His father often goes on business by car

=> How does his father often go business?

6. Lan and Hoa are going to visit Ha Long Bay for two days

=> How long are Lan and Hoa going to visit Ha Long Bay?

7. Khoa is the tallest boy in this school

=> Who is the tallest boy in this school?

8. The Great Wall of China is 12 meters high

=> How high is the Great Wall of China?

9. He goes to the movies three times a month

=> How often does he go to the movies?

10. My uncle can't go to work because he has a broken leg

 => Why does your uncle can't go to work?

1. I couldn't bring my homework because my dog ate my homework

2. Because I am too busy, I don't exercise (Câu này lạ)

3. Because I have too much homework, I go to bed late

4. Because I can't give up smoking, I will put on weight.

5. I lost my friend's book because I was careless.

6. I'm not going to go to the beach because I have to take an exam.

1. Listen! Some one (cry) is crying in the next room.

2. Is your brother (sit) sitting next to the beautiful girl over there at present?

3. Now they (try) are trying to pass the examination

4. It's 12 o'clock , and my parents (cook) are cooking lunch in the kitchen.

1. He is enough strong to carry the heavy luggage

=> He is strong enough to carry the heavy luggage

2. I'd like buying a new dictionary but I don't have enough money

=>I'd like to buy a new dictionary but I don't have enough money 

3. I recently visited the school where I used to studying five years ago

=> I recently visited the school where I used to study five years ago

4. My brother are going to study in New York next month

=> My brother is going to study in New York next month

5. We used to see a movie called "King Kong" last summer.

=> We saw a movie called "King Kong" last summer.

1. It's / I / heard / not / as / good / it / was / as / before

=> It's not as good as I was heard it before.

2. are / they / plans / making / for / weekend.

=> They are making for weekend plans.

3. There / be / will / a / concert / music / Teacher's / day / on

=> There will be a music concert on Teacher's day.

4. the / first / time / it / I / is / have / this / food / eaten/

=> It is the first time I have eatten this food.

5.  visited / she / when / Nha Trang / she / a / was / girl / little

=> She visited Nha Trang when she was a little girl.