thank you teacher

thanks teacher

Bài 5

\(a - b = 2 <=> b = a - 2\)

Do đó: \(P = 3a^2 + (a-2)^2 + 8\)

\(= 3a^2 + a^2 - 4a + 4 + 8\)

\(= 4a^2 - 4a + 12\)

\(= (2a - 1)^2 + 11\)

Vì \((2a - 1)^2 \geq 0 \) với mọi a nên \(= (2a - 1)^2 + 11 \geq 11 \) hay \(P \geq 11\)

Dấu "=" xảy ra \(\begin{cases} a - b = 2 \\ 2a - 1 = 0 \\\end{cases} <=> \begin{cases} a = \dfrac{1}{2} \\ b = -\dfrac{3}{2} \\\end{cases}\)

Vậy giá trị nhỏ nhất của P là 11 tại \(\begin{cases} a = \dfrac{1}{2} \\ b = -\dfrac{3}{2} \\\end{cases}\)

câu hình:

a) Vì AB là đường kính \(\Rightarrow\angle ADB=90\Rightarrow\angle EDB+\angle EHB=180\)

\(\Rightarrow EDHB\) nội tiếp

b) Xét \(\Delta AHE\) và \(\Delta ADB:\) Ta có: \(\left\{{}\begin{matrix}\angle DABchung\\\angle AHE=\angle ADB=90\end{matrix}\right.\)

\(\Rightarrow\Delta AHE\sim\Delta ADB\left(g-g\right)\Rightarrow\dfrac{AH}{AD}=\dfrac{AE}{AB}\Rightarrow AB.AH=AD.AE\)

mà \(AH.AB=AC^2\) (hệ thức lượng) \(\Rightarrow AC^2=AD.AE\)

c) Vì \(EF\parallel AB\) \(\Rightarrow\angle CFE=\angle CBA=\angle CDA=\angle CDE\)

\(\Rightarrow CDFE\) nội tiếp mà \(\angle CEF=90\) \((EF\parallel AB,AB\bot CH)\)

\(\Rightarrow\angle CDF=90\Rightarrow CD\bot DF\)

Vì \(\Delta CDF\) vuông tại D có K là trung điểm CF \(\Rightarrow KC=KD\)

\(\Rightarrow\Delta KCD\) cân tại K \(\Rightarrow\angle DKB=2\angle DCB=2\angle DAB=\angle DOB\)

\(\Rightarrow DKOB\) nội tiếp \(\Rightarrow K\in\left(OBD\right)\)

Câu 1

1) \(A=\sqrt{20}-\sqrt{45}+\sqrt{6+2\sqrt{5}}\)

\(=2\sqrt{5}-3\sqrt{5}+\sqrt{\left(\sqrt{5}\right)^2+2\sqrt{5}+1}\)

\(=-\sqrt{5}+\sqrt{\left(\sqrt{5}+1\right)^2}\)

\(=-\sqrt{5}+\sqrt{5}+1\)

\(=1\)

2) ĐKXĐ: \(x>0;x\ne1\)

\(B=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)^2}\)

\(=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{1}{\sqrt{x}-1}\right).\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}+1}\)

\(=\dfrac{1+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}.\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}+1}\)

\(=\dfrac{\sqrt{x}-1}{\sqrt{x}}\)

\(\Rightarrow B=\dfrac{\sqrt{x}-1}{\sqrt{x}}=\dfrac{1}{2}\)

\(\Leftrightarrow2\left(\sqrt{x}-1\right)=\sqrt{x}\)

\(\Leftrightarrow2\sqrt{x}-2=\sqrt{x}\)

\(\Leftrightarrow2\sqrt{x}-\sqrt{x}=2\)

\(\Leftrightarrow\sqrt{x}=2\)

\(\Rightarrow x=4\left(tmđk\right)\)

Câu 5 :

Ta có : \(6a+3b+2c=abc\) \(\Rightarrow\dfrac{6}{bc}+\dfrac{3}{ac}+\dfrac{2}{ab}=1\)

Đặt : \(\left\{{}\begin{matrix}\dfrac{1}{a}=x\\\dfrac{2}{b}=y\\\dfrac{3}{c}=z\end{matrix}\right.\) với \(x,y,z>0\) \(\Rightarrow xy+yz+zx=1\)

Ta biến đổi : \(\dfrac{1}{\sqrt{a^2+1}}=\sqrt{\dfrac{\dfrac{1}{a^2}}{1+\dfrac{1}{a^2}}}=\sqrt{\dfrac{x^2}{1+x^2}}=\sqrt{\dfrac{x^2}{xy+xz+yz+x^2}}=\sqrt{\dfrac{x^2}{\left(x+y\right)\left(x+z\right)}}\)

Chứng minh tương tự ta có :

\(\dfrac{1}{\sqrt{b^2+4}}=\sqrt{\dfrac{y^2}{\left(y+z\right)\left(y+x\right)}}\) ; \(\dfrac{1}{\sqrt{c^2+9}}=\sqrt{\dfrac{z^2}{\left(z+x\right)\left(z+y\right)}}\)

Do đó : \(Q=\sqrt{\dfrac{x^2}{\left(x+z\right)\left(x+y\right)}}+\sqrt{\dfrac{y^2}{\left(y+z\right)\left(y+x\right)}}+\sqrt{\dfrac{z^2}{\left(z+x\right)\left(z+y\right)}}\)

Áp dụng BĐT Cô - si ta được :

\(Q=\sqrt{\dfrac{x^2}{\left(x+z\right)\left(x+y\right)}}+\sqrt{\dfrac{y^2}{\left(y+z\right)\left(y+x\right)}}+\sqrt{\dfrac{z^2}{\left(z+x\right)\left(z+y\right)}}\)

\(\le\dfrac{1}{2}\left(\dfrac{x}{x+z}+\dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{y}{y+x}+\dfrac{z}{z+x}+\dfrac{z}{z+y}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{x+z}{x+z}+\dfrac{x+y}{x+y}+\dfrac{z+y}{z+y}\right)=\dfrac{1}{2}\cdot3=\dfrac{3}{2}\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}a=\sqrt{3}\\b=2\sqrt{3}\\c=3\sqrt{3}\end{matrix}\right.\)

Vậy Max \(P=\dfrac{3}{2}\) khi \(\left\{{}\begin{matrix}a=\sqrt{3}\\b=2\sqrt{3}\\c=3\sqrt{3}\end{matrix}\right.\)

Câu 2

1) Phương trình \(x^2-6x+5=0\) có:

\(a+b+c=1-6+5=0\)

\(\Rightarrow\) Phương trình có hai nghiệm phân biệt \(x_1=1\) và \(x_2=\dfrac{c}{a}=5\)

2) \(\left\{{}\begin{matrix}2\left(x+2\right)=3\left(y-1\right)\\3x+y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+4=3y-3\\3x+y=6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-3y=-7\\3x+y=6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-3y=-7\\9x+3y=18\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}11x=11\\3x+y=6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\3+y=6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=3\end{matrix}\right.\)

1:  Only with careful environmental planning can we protect the world in which we live.

D.  We can protect the world we live in only with careful environmental planning.

2:  You should take regular exercises instead of sitting in front of the television all day.

A.  Taking regular exercises is better than sitting in front of the television all day.

3:  It was not until after I got home that I realized I had not set the burglar alarm in the office.

C.  I didn’t turn the burglar alarm on before I left the office, but I only became aware of this after I'd arrived home.

4:  He did not remember the meeting. He went out for a coffee with his friends then.

D.  Not remembering the meeting, he went out for a coffee with his friends.

5:  They left their home early. They didn’t want to miss the first train.

C.  They left their home early so as not to miss the first train.

6:  I’m sure Luisa was very disappointed when she failed the exam

B.  Luisa must have been very disappointed when she failed the exam.

7.  “You had better see a doctor if the sore throat does not clear up.” she said to me.

D.  She suggested that I see a doctor if the sore throat did not clear up.

8:  Without her teacher’s advice, she would never have written such a good essay

C.  She wrote a good essay as her teacher gave her some advice.

9.  She tried very hard to pass the driving test. She could hardly pass it.

C.  No matter how hard she tried, she could hardly pass the driving test.

10. Mary loved her stuffed animal when she was young. She couldn’t sleep without it.

A. When Mary was young, she loved her stuffed animal so much that she couldn't sleep without it.

1:  Only with careful environmental planning can we protect the world in which we live.

A.  Careful environmental planning protects the world we live in.

B.  Planning the environment carefully, we can protect the world in which we live.

C.  Protecting the world we live in, we plan the environment carefully.

D.  We can protect the world we live in only with careful environmental planning.

2:  You should take regular exercises instead of sitting in front of the television all day.

A.  Taking regular exercises is better than sitting in front of the television all day.

B.  Sitting in front of the television all day helps you take regular exercises.

C.  Sitting in front of the television all day and taking exercises are advisable.

D.  Don’t take regular exercises, just sit in front of the television all day.

3:  It was not until after I got home that I realized I had not set the burglar alarm in the office.

A.  On the way home, I suddenly realized that I had forgotten to turn on the burglar alarm in the office.

B.  Fortunately, I realized that I hadn't set the burglar alarm just before I left for home; otherwise, I would have had to travel all the way back to the office.

C.  I didn’t turn the burglar alarm on before I left the office, but I only became aware of this after I'd arrived home.

D. I wish I had realized before I arrived home that I hadn't turned on the burglar alarm in the office, then it would have been easier to go and set it.

4:  He did not remember the meeting. He went out for a coffee with his friends then.

A.  Not remember the meeting, he went out for a coffee with his friends.

B.  Not to remember the meeting, he went out for a coffee with his friends.

C.  Not remembered the meeting, he went out for a coffee with his friends.

D.  Not remembering the meeting, he went out for a coffee with his friends.

5:  They left their home early. They didn’t want to miss the first train.

A.  They left their home early so as to not miss the first train.

B.  They left their home early for fear that they wouldn’t miss the first train.

C.  They left their home early so as not to miss the first train.

D.  They left their home early in order that not to miss the first train.

6:  I’m sure Luisa was very disappointed when she failed the exam

A.  Luisa must be very disappointed when she failed the exam.

B.  Luisa must have been very disappointed when she failed the exam.

C. Luisa may be very disappointed when she failed the exam.

D. Luisa could have been very disappointed when she failed the exam.

1:  Only with careful environmental planning can we protect the world in which we live.

D.  We can protect the world we live in only with careful environmental planning.

2:  You should take regular exercises instead of sitting in front of the television all day.

A.  Taking regular exercises is better than sitting in front of the television all day.

3:  It was not until after I got home that I realized I had not set the burglar alarm in the office.

C.  I didn’t turn the burglar alarm on before I left the office, but I only became aware of this after I'd arrived home.

4:  He did not remember the meeting. He went out for a coffee with his friends then.

D.  Not remembering the meeting, he went out for a coffee with his friends.

5:  They left their home early. They didn’t want to miss the first train.

C.  They left their home early so as not to miss the first train.

D.  They left their home early in order that not to miss the first train.

6:  I’m sure Luisa was very disappointed when she failed the exam

B.  Luisa must have been very disappointed when she failed the exam.

thank you so much

ra 1 bài anh đi cô lớp 7 đi cô

để cho em thử sức viết 

Cảm ơn cô:33

thank you so much!!!!!!!!!!!!!!!!

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I. Change into passive.

1.  John collects money.

 .................................................................................................................................... 

2.  Anna opened the window.  

 .................................................................................................................................... 

3.  We have done our homework.

 .................................................................................................................................... 

4.  I will ask a question.  

 .................................................................................................................................... 

5.  He can cut out the picture.  

.................................................................................................................................... 

6.  The sheep ate a lot.  

 .................................................................................................................................... 

7.  We do not clean our rooms.

 .................................................................................................................................... 

8.  William will not repair the car.

 .................................................................................................................................... 

9.  Did Sue draw this circle?  

 .................................................................................................................................... 

10. Could you feed the dog?

 .................................................................................................................................... 

II: Rewrite these following sentences with the same meaning
1. She said, "I am reading."
→ She said that…………………………………………………………….
2. They said, "We are busy."
→ They said that ……………………………………………………………….
3. He said, "I know a better restaurant."
→ He said that………………………………………………………………...
4. She said, "I woke up early."
→ She said that……………………………………………………………….
5. He said, "I will ring her."
→ He said that………………………………………………………………….
6. They said, "We have just arrived."
→ They said that………………………………………………………………
7. He said, "I will clean the car."
→ He said that……………………………………………………………….
8. She said, "I did not say that."
→ She said that…………………………………………………………….
9. She said, "I don't know where my shoes are."
→ She said that……………………………………………………………….
10. He said: "I won't tell anyone."
→ He said that………………………………………………………………

thanks you

thanks for your help

Đề tỉnh khác khó quá, không biết đề tỉnh e ra sao :v, đang chờ các e thi

đề sáng ni zừa thi xog nek 

lạy trời câu cuối(:((()