Rffsdffdsff

Tham khảo nha, tuy ko trùng đề lắm

Gọi trung điểm dường cheo AC, BD lần lượt là M, N
MN cắt AB, CD lần lượt ở I, K
Ta cần chứng minh góc NIB = góc MKC
Lấy H là trung điểm BC. Nối MH, NH. 
Xét tam giac ABC có AM = MC ; CH = HB => MH là đường trung bình tam giác ABC => MH =AB/2 (1) và MH // AB => góc KMH = góc INH (2)
chung minh tuong tu ta có: NH = CD/2 (3)và NH // CD =>góc INH = góc MKC (4)
Mat khac từ (1)và (3) ta có NH = MH vì đều bằng một nửa AB và CD => tam giác MHN cân tại H => góc NMH = góc MNH =>góc KMH = góc INH (vì kể với 2 góc bằng nhau) (5)
Từ (3)(4)(5) => góc MKC = góc NIB (đpcm)

góc MKC =  NIB (đpcm)

 Vì \(P\left(x\right)⋮\left(2x-1\right)\) \(\Rightarrow P\left(\dfrac{1}{2}\right)=0\)

 Xét đa thức \(Q\left(x\right)=P\left(x\right)-\left(x+1\right)\). Ta có \(Q\left(1\right)=Q\left(2\right)=Q\left(3\right)=Q\left(4\right)=0\) nên \(Q\left(x\right)\) có 4 nghiệm là \(1,2,3,4\). Nếu \(Q\left(x\right)\equiv0\) thì \(P\left(x\right)=x+1\), vô lý. Do đó \(Q\left(x\right)\) là đa thức khác hằng \(\Rightarrow\) bậc của \(Q\left(x\right)\) phải lớn hơn hoặc bằng 4. Mà \(P\left(x\right)\) có hệ số cao nhất là 1 \(\Rightarrow\) \(Q\left(x\right)\) cũng phải có hệ số cao nhất là 1.

 Mặt khác, \(Q\left(\dfrac{1}{2}\right)=P\left(\dfrac{1}{2}\right)-\left(\dfrac{1}{2}+1\right)=-\dfrac{3}{2}\)

 Đặt \(Q\left(x\right)=\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)R\left(x\right)\). Khi đó \(R\left(x\right)\) có hệ số cao nhất là 1 và \(R\left(\dfrac{1}{2}\right)=-\dfrac{8}{35}\).

 Khi đó, ycbt \(\Leftrightarrow\) tìm tất cả các đa thức \(R\left(x\right)\) có hệ số cao nhất là 1 mà \(R\left(\dfrac{1}{2}\right)=-\dfrac{8}{35}\).

 Nếu \(R\left(x\right)=-\dfrac{8}{35}\) thì vô lý.

 Nếu \(R\left(x\right)\) có bậc là 1 thì \(R\left(x\right)=x+a\). Thế \(x=\dfrac{1}{2}\) sẽ tìm được \(a=-\dfrac{51}{70}\) và do đó \(R\left(x\right)=x-\dfrac{51}{70}\) \(\Rightarrow Q\left(x\right)=\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)\left(x-\dfrac{51}{70}\right)\). Thế vào \(Q\left(x\right)=P\left(x\right)-\left(x+1\right)\) ta tìm được đa thức \(P\left(x\right)\) thỏa ycbt.

 Nếu \(R\left(x\right)\) có bậc 2 thì \(R\left(x\right)=x^2+ax+b\). Thế \(x=\dfrac{1}{2}\) thì ta có \(\dfrac{1}{2}a+b=-\dfrac{1}{2}\), sẽ có vô số cặp số \(\left(a,b\right)\) thỏa mãn điều này \(\Rightarrow\) tồn tại vô số đa thức \(Q\left(x\right)\) \(\Rightarrow\) tồn tại vô số đa thức \(P\left(x\right)\) thỏa ycbt.

 Tương tự như thế, ta xét bậc của \(R\left(x\right)\) tăng dần thì sẽ có vô số đa thức \(P\left(x\right)\) thỏa mãn ycbt. (nhưng sẽ không có công thức chung cho các đa thức)

Vì $P\left(x\right)⋮\left(2x-1\right)$ ⇒�(12)=0⇒P(21​)=0

 Xét đa thức $Q\left(x\right)=P\left(x\right)-\left(x+1\right)$. Ta có $Q\left(1\right)=Q\left(2\right)=Q\left(3\right)=Q\left(4\right)=0$ nên $Q\left(x\right)$ có 4 nghiệm là $1,2,3,4$. Nếu $Q\left(x\right)\equiv 0$ thì $P\left(x\right)=x+1$, vô lý. Do đó $Q\left(x\right)$ là đa thức khác hằng $\Rightarrow$ bậc của $Q\left(x\right)$ phải lớn hơn hoặc bằng 4. Mà $P\left(x\right)$ có hệ số cao nhất là 1 $\Rightarrow$ $Q\left(x\right)$ cũng phải có hệ số cao nhất là 1.

 Mặt khác, �(12)=�(12)−(12+1)=−32Q(21​)=P(21​)−(21​+1)=−23​

 Đặt $Q\left(x\right)=\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)R\left(x\right)$. Khi đó $R\left(x\right)$ có hệ số cao nhất là 1 và �(12)=−835R(21​)=−358​.

 Khi đó, ycbt $\iff$ tìm tất cả các đa thức $R\left(x\right)$ có hệ số cao nhất là 1 mà �(12)=−835R(21​)=−358​.

 Nếu �(�)=−835R(x)=−358​ thì vô lý.

 Nếu $R\left(x\right)$ có bậc là 1 thì $R\left(x\right)=x+a$. Thế �=12x=21​ sẽ tìm được �=−5170a=−7051​ và do đó �(�)=�−5170R(x)=x−7051​ ⇒�(�)=(�−1)(�−2)(�−3)(�−4)(�−5170)⇒Q(x)=(x−1)(x−2)(x−3)(x−4)(x−7051​). Thế vào $Q\left(x\right)=P\left(x\right)-\left(x+1\right)$ ta tìm được đa thức $P\left(x\right)$ thỏa ycbt.

 Nếu $R\left(x\right)$ có bậc 2 thì �(�)=�2+��+�R(x)=x2+ax+b. Thế �=12x=21​ thì ta có 12�+�=−1221​a+b=−21​, sẽ có vô số cặp số $\left(a,b\right)$ thỏa mãn điều này $\Rightarrow$ tồn tại vô số đa thức $Q\left(x\right)$ $\Rightarrow$ tồn tại vô số đa thức $P\left(x\right)$ thỏa ycbt.

 Tương tự như thế, ta xét bậc của $R\left(x\right)$ tăng dần thì sẽ có vô số đa thức $P\left(x\right)$ thỏa mãn ycbt. (nhưng sẽ không có công thức chung cho các đa thức)

1. This is the best smoothie I’ve ever drink.

I’ve never had drunk such a better smoothie before

2. Lien’s hair is as long as my hair.

Lien’s hair is the same length of my hair

3. Hong is the most pretty person in my class.

Hong is more pretty than anyone else in my class .

4. Do you have a ruler thinner than this ruler?

Is this ruler thinnest you have?

5. The white car is more expensive than the blue car.

The blue car is not as expensive as the white car/The blue car is less cheap than the white car.

6. There is no one better than my mother.

My mother is the best person/woman/lady .

7. Tom can swim much faster than Mary. (AS)

Mary can’t swim as fast as Tom (can/do)

8. My pen isn’t as high as yours. (THAN)

Your pen is higher than mine 

9. My salary isn’t as high as you think. (THAN)

My salary is lower than you think

10. Prison food isn’t as bad as I expected. (THAN)

Prison food is better than I expected

11. Mary isn’t reliable as she used to be. (MORE)

Mary is not more reliable than she does now.

12. I’m not as heavy as I used to be. (LIGHTER)

I’m lighter than I used to be

13. You are more polite than Tom. (RUDE)

You are ruder than Tom

14. Tom and Mary aren’t as young as they say they are. (THAN)

Tom and Mary are older than they say they are.

15. The fracture wasn’t as serious as we thought (LESS)

The fracture was less serious than we thought

16. Tom is a bit shorter than Mary. (LITTLE)

Mary is a little taller than Tom

17. Tom said doing that was more difficult than he expected. (LESS) 

Tom said doing that was less easy than he expected

18. I was richer than my neighbours. (POOR)

I wasn’t poorer than my neighbours.

1. This is the best smoothie I’ve ever drink.

I’ve never had drunk such a better smoothie before

2. Lien’s hair is as long as my hair.

Lien’s hair is the same length of my hair

3. Hong is the most pretty person in my class.

Hong is more pretty than anyone else in my class .

4. Do you have a ruler thinner than this ruler?

Is this ruler thinnest you have?

5. The white car is more expensive than the blue car.

The blue car is not as expensive as the white car/The blue car is less cheap than the white car.

6. There is no one better than my mother.

My mother is the best person/woman/lady .

7. Tom can swim much faster than Mary. (AS)

Mary can’t swim as fast as Tom (can/do)

8. My pen isn’t as high as yours. (THAN)

Your pen is higher than mine 

9. My salary isn’t as high as you think. (THAN)

My salary is lower than you think

10. Prison food isn’t as bad as I expected. (THAN)

Prison food is better than I expected

11. Mary isn’t reliable as she used to be. (MORE)

Mary is not more reliable than she does now.

12. I’m not as heavy as I used to be. (LIGHTER)

I’m lighter than I used to be

13. You are more polite than Tom. (RUDE)

You are ruder than Tom

14. Tom and Mary aren’t as young as they say they are. (THAN)

Tom and Mary are older than they say they are.

15. The fracture wasn’t as serious as we thought (LESS)

The fracture was less serious than we thought

16. Tom is a bit shorter than Mary. (LITTLE)

Mary is a little taller than Tom

17. Tom said doing that was more difficult than he expected. (LESS) 

Tom said doing that was less easy than he expected

18. I was richer than my neighbours. (POOR)

I wasn’t poorer than my neighbours.

Ta thấy 

\(f\left(x\right):g\left(x\right)\)

\(\Rightarrow\left(x^{100}+x^{99}+x^{98}+x^5+2020\right):\left(x^2-1\right)\)

\(=\left(x^{98}+x^{97}+2x^{96}+2x^{95}+...2x^4+3x^3+2x^2+3x+2\right)\) có số dư là \(R\left(x\right)=3x+2022\)

\(\Rightarrow R\left(2021\right)=3.2021+2022=8085\)

\(8x^3-12x^2+6x-1=\left(2x-1\right)^3\)

1. It is such an interesting film that we have seen it twice.
2. It is such a happy girl that she sings many songs.
3. He is such a good boy that everyone loves him.
4. It is such a very modern house that everybody likes it.