Khối lượng 1 viên gạch =1 Kg

Cho tam giác ABC vuông tại a . Điểm M bất kì trên AC . Kẻ CH vuông góc với tia BM tại H và tia BA tại O. Gọi I là trung điểm của BC . Qua M kẻ đường thẳng vuông góc với MI , cắt OB và OC thứ tự tại P và Q . Chứng minh M là trung điểm của PQ

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a, \(x^2+2y^2+z^2\ge2xy-2yz\)

\(\Leftrightarrow x^2-2xy+y^2+y^2+2yz+z^2\ge0\)

\(\Leftrightarrow\left(x-y\right)^2+\left(y+z\right)^2\ge0\)* đúng *

Dấu ''='' xảy ra khi \(x=y=-z\)

b, \(x^2+y^2+z^2+14\ge2x-4y+6z\)

\(\Leftrightarrow x^2-2x+1+y^2-4y+4+z^2-6z+9\ge0\)

\(\Leftrightarrow\left(x-1\right)^2+\left(y-2\right)^2+\left(z-3\right)^2\ge0\)*đúng *

Dấu ''='' xảy ra khi \(x=1;y=2;z=3\)

a) chuyển VP rồi tách 2y² -> y² + y² ta đc bđt luôn đúng ( x - y )² + ( y + z )² ≥ 0 

Đẳng thức xảy ra <=> x = y = -z

b) chuyển VP rồi tách 14 = 1 + 4 + 9 ta đc bđt luôn đúng ( x - 1 )² + ( y + 2 )² + ( z - 3 )² ≥ 0

Đẳng thức xảy ra <=> x = 1 ; y = -2 ; z = 3

1, B

2, A

3, D

4, D

5, B

6, C 

7, C

8, B

9, A

10, B

* Nếu mình sai câu nào thì thày Hoàng Anh sẽ sửa nhé!

1.b

2.a

3.d

4.d

5.b

6.c

7.c

8.b

9.a

10.b

1, D

2,D

3, A

4, A

5,D

6, A

7, C

8,  A

9, D

10, A

1. D

2.D 

3. A

4. A

5.D

6. A

7.C

8.A

9. D

10. A

1.You / smoke / you / get yellow teeth

=> If you smoke, you get yellow teeth

2.Children / play outside / they / not get overweight. 

=> If the children not play outside, they not get overweight

3.You / heat ice / it / melt.

=> If you heat ice, it melt

4.I /speak to john / he / get annoyed. 

=> If I speak to John, he get annoyed

5.Lots of people / come/ Jenny / have a party.

=> if lots of people come, Jenny has a party 

6.I / feel good the next day / I / go to bed early.

=> I feel good the next day, if I go to bed early

7.She / buy expensive clothes / she / go shopping.

=> She buy expensive clothes if she go shopping

8.My daughter / pass her exams / she / work hard.

=> My daughter passed her exam because she had worked hard.

9.David / be sick / he / drink milk

=> David'll be sick if he drinks milk.

10.The river / freeze / it / be very cold.

=> The river froze because it was very cold.

11.I / to visit the museums / I / be in a new city.

=> I would to visit the museums if I was in a new city.

12.I / cycle to work / the weather / be fine.

=> I will cycle to work if the weather is fine.

13.My flatmate / clean it really well / she / clean the house.

=> My flatmate cleans it very well when she is cleaning the house.

14.Everybody / be grumpy / it / rain a lot.

=> Everybody will be grumpy if it rains a lot.

1. If you smoke, you'll get yellow tooth.

2. Children should play outside if they don't want to get overweight.

3. If you heat ice, it melts.

4. If I speak to John, he'll be annoyed.

5. Lots of people came to Jenny's house to have a party.

6. If I want to feel good the next day, I should go to bed early.

7. She bought expensive clothes while she was going shopping.

8. My daughter passed her exam because she had worked hard.

9. David'll be sick if he drinks milk.

10. The river froze because it was very cold.

11. I would to visit the museums if I was in a new city.

12. I will cycle to work if the weather is fine.

13. My flatmate cleans it very well when she is cleaning the house.

14. Everybody will be grumpy if it rains a lot.

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