Câu 2: 

\(A=x^2-10x+1\\ =\left(x^2-10x+25\right)-24\\ =\left(x-5\right)^2-24\ge-24\forall x\)

Dấu "=" xảy ra: `x-5=0<=>x=5` 

\(B=x^2-5x+2\\ =\left(x^2-5x+\dfrac{25}{4}\right)-\dfrac{17}{4}\\ =\left(x^2-2\cdot x\cdot\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2\right)-\dfrac{17}{4}\\ =\left(x-\dfrac{5}{2}\right)^2-\dfrac{17}{4}\ge-\dfrac{17}{4}\forall x\)

Dấu "=" xảy ra: `x-5/2=0<=>x=5/2` 

Câu 2

A = x² - 10x + 1

= x² + 2.x.5 + 25 - 24

= (x + 5)² - 24

Do (x + 5)² ≥ 0 với mọi x ∈ R

⇒ (x + 5)² - 24 ≥ -24 (với mọi x ∈ R)

Vậy GTNN của A là -24 khi x = -5

B = x² - 5x + 2

Bạn xem lại đề, là $13x^3$ hay $13x^2$ vậy?

Lời giải:
Trước hết ta cần nắm 1 số tính chất:

- Một scp lẻ khi chia 8 dư 1 (bạn có thể xét mô đun 4 của số đó để chứng minh)

- Một scp khi chia 5 dư $0,1$ hoặc $4$.

----------------------

Ta có: $2n+7$ là scp lẻ nên $2n+7\equiv 1\pmod 8$

$\Rightarrow 2n+6\equiv 0\pmod 8$

$\Rightarrow n+3\equiv 0\pmod 4$

$\Rightarrow n$ lẻ. 

$\Rightarrow 3n+10$ cũng là scp lẻ.

$\Rightarrow 3n+10\equiv 1\pmod 8$

$\Rightarrow 3n+9\equiv 0\pmod 8$

$\Rightarrow 3(n+3)\equiv 0\pmod 8\Rightarrow n+3\equiv 0\pmod 8(*)$

Lại có:

Đặt $2n+7=a^2, 3n+10=b^2$ với $a,b$ là số tự nhiên.

$\Rightarrow 2n+7+3n+10=a^2+b^2$

$\Rightarrow a^2+b^2=5n+17\equiv 2\pmod 5$

Ta thấy $a^2\equiv 0,1,4\pmod 5; b^2\equiv 0,1,4\pmod 5$

Do đó để $a^2+b^2\equiv 2\pmod 5$ thì chỉ khi $a^2, b^2\equiv 1\pmod 5$

$\Rightarrow 3n+10\equiv 1\pmod 5$

$\Rightarrow 3n+9\equiv 0\pmod 5$

$\Rightarrow 3(n+3)\equiv 0\pmod 5$

$\Rightarrow n+3\equiv 0\pmod 5(**)$

Từ $(*); (**)$ mà $(5,8)=1$ nên $n+3\vdots 40$.

Yesterday, I went to (1) the park with my friends. We had a picnic under (2) a big tree and played frisbee. In the afternoon, we went for (3) a walk around the lake. We saw (4) an interesting bird that we had never seen before. It had (5) a bright red beak and (6) a long tail. We also saw the ducks swimming in the lake. After our walk, we had (7) an ice cream cone and then went (8) chỗ này không cần điền home

21. finishes (lịch trình có sẵn -> THì HTĐ, chủ ngữ số ít)

22. to design (prefer + to V: Chỉ sở thích | prever + V(ing) + to V(ing): thích làm gì hơn làm gì)

23. hates (Chỉ sở thích -> HTĐ, chủ ngữ số ít)

24. doesn't like (Chỉ sở thích -> thì HTĐ, chủ ngữ số ít, thể phủ định đi với doesn't)

25. Does ... start (Lịch trình có sẵn -> Thì HTĐ, thể câu hỏi chủ ngữ số ít đi với does, động từ chính đứng sau chủ ngữ và nguyên thể)

21will finish 22 designing 23hates 24doesn't like 25Will /start

1. don't stay

2. don't wash

3. doesn't do

4. don't go

5. doesn't open

6. doesn't eat

7. don't chat

8. doesn't use

9. don't skate

10. doesn't throw

1. I don’t stay/ doesn’t stay at home.

2. We don’t wash/ doesn’t wash the family car.

3. Doris don’t do/ doesn’t do her homework.

4. They don’t go/ doesn’t go to bed at 8.30 p.m.

5. Kevin don’t open/ doesn’t open his workbook.

6. Our hamster don’t eat/ doesn’t eat apples.

7. You don’t chat/ doesn’t chat with your friends.

8. She don’t use/ doesn’t use a ruler.

9. Max, Frank and Steve don’t skate/ doesn’t skate in the yard.

10. The boy don’t throw/ doesn’t throw stones.

1 am writing

2 seems

3 are taking

4 are losing

5 live

6 is changing

7 are building

8 belongs

9 don't understand

10 don't do

11 don't care

12 am thinking

13 appears

14 gets

1 luggage

2 discoveries

3 advice - attorneys

4 furniture

5 teeth

6 Thieves

7 hair

8 oxen

9 pianos

10 medium

11 belief

12 matches

13 information

14 working

15 deers

Minh doesn't usually sleep early at weekends

Do you understand the questions from your teacher?

Her husband and his colleague play tennis whenever they are free

My family normally eat breakfast at 6.30

San doesn't phone her/his mother every Mondays

1 Minh doesn't usually sleep early at weekends

2 Do you understand the question from your teacher?

3 Her husband and his colleagur play tennis whenever they are free

4 My family normally eats breakfast at 6.30

5 San doesn't phone her mother on Mondays