1) \(\sqrt{2x-5}=7\)

\(\left(\sqrt{2x-5}\right)^2=7^2\)

\(2x-5=49\)

\(2x=54\)

\(x=27\)

2) \(3+\sqrt{x-2}=4\)

\(\sqrt{x-2}=1\)

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

\(x-2=1\)

\(x=3\)

1) \(\sqrt{2x-5}=7\left(đk:x\ge\dfrac{5}{2}\right)\)

\(\Leftrightarrow2x-5=49\Leftrightarrow2x=54\Leftrightarrow x=27\left(tm\right)\)

2) \(3+\sqrt{x-2}=4\left(đk:x\ge2\right)\)

\(\Leftrightarrow\sqrt{x-2}=1\Leftrightarrow x-2=1\Leftrightarrow x=3\)

3) \(\Leftrightarrow\sqrt{\left(x-1\right)^2}=1\Leftrightarrow\left|x-1\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

4) \(\Leftrightarrow\sqrt{\left(x-2\right)^2}=1\Leftrightarrow\left|x-2\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

5) \(\Leftrightarrow\sqrt{\left(2x-1\right)^2}=\sqrt{\left(x+4\right)^2}\)

\(\Leftrightarrow\left|2x-1\right|=\left|x+4\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=x+4\\2x-1=-x-4\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)

6) \(ĐK:x\ge-2\)

 \(\Leftrightarrow5\sqrt{x+2}-3\sqrt{x+2}-\sqrt{x+2}=\sqrt{x+7}\)

\(\Leftrightarrow\sqrt{x+2}=\sqrt{x+7}\)

\(\Leftrightarrow x+2=x+7\Leftrightarrow2=7\left(VLý\right)\)

Vậy \(S=\varnothing\)

7) \(ĐK:x\ge-1\)

\(\Leftrightarrow5\sqrt{2x+1}+3\sqrt{x+1}=4\sqrt{x+1}+4\sqrt{2x+1}\)

\(\Leftrightarrow\sqrt{2x+1}=\sqrt{x+1}\)

\(\Leftrightarrow2x+1=x+1\Leftrightarrow x=0\left(tm\right)\)

\(3,\sqrt{x^2-2x+1}=1\left(x\in R\right)\\ \Leftrightarrow\sqrt{\left(x-1\right)^2}=1\\ \Leftrightarrow\left|x-1\right|=1\Leftrightarrow\left[{}\begin{matrix}x-1=1\left(x\ge1\right)\\x-1=-1\left(x< 1\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=0\left(tm\right)\end{matrix}\right.\)

\(4,ĐK:x\in R\\ PT\Leftrightarrow\sqrt{\left(x-2\right)^2}=1\\ \Leftrightarrow\left|x-2\right|=1\Leftrightarrow\left[{}\begin{matrix}x-2=1\left(x\ge2\right)\\x-2=-1\left(x< 2\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=1\left(tm\right)\end{matrix}\right.\)

\(5,ĐK:x\in R\\ PT\Leftrightarrow\left|2x-1\right|=\left|x+4\right|\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=x+4\\1-2x=x+4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)

\(6,ĐK:x\ge-2\\ PT\Leftrightarrow5\sqrt{x+2}-3\sqrt{x+2}-\sqrt{x+2}=\sqrt{x+7}\\ \Leftrightarrow\sqrt{x+2}=\sqrt{x+7}\Leftrightarrow x+2=x+7\Leftrightarrow0x=5\Leftrightarrow x\in\varnothing\)

\(7,ĐK:x\ge-1\\ PT\Leftrightarrow5\sqrt{x+2}+3\sqrt{x+1}=4\sqrt{x+1}+4\sqrt{x+2}\\ \Leftrightarrow\sqrt{x+2}=\sqrt{x+1}\\ \Leftrightarrow x+2=x+1\\ \Leftrightarrow0x=-1\Leftrightarrow x\in\varnothing\)

Huhu sao ko ai tin e vậy

chữ xấu quá khum đọc đc

9:

a: XétΔABC vuông tại A và ΔHBA vuông tại H có

góc B chung

=>ΔABC đồng dạng với ΔHBA

=>BA/BH=BC/BA
=>BA^2=BH*BC

b: BC=25cm; AB=căn 9*25=15cm; AC=căn 16*25=20cm

S ABC=1/2*15*20=150cm²

C ABC=25+15+20=60cm

a, Vì D,M là trung điểm AB,AC nên DM là đtb tg ABC

Do đó \(DM=\dfrac{1}{2}BC=\dfrac{7}{2}\left(cm\right)\) và DM//BC

8. The examiners  have to read the passage 3 times.

The passage has to be read 3 times by the examiners

12.They will have to pull down that building.

That building will have to be pulled down

17. You should pay more attention to your study.

Your study should be paid more attention to

18.They can see the valley from the top of this hill.

The valley can be seen from the top of this hill

19.You must wash your hands.

Your hands must be washed

20. Will you post this letter on the way to work?

Will this letter be posted on the way to work by you?

22. How many ways can you solve this problem?

How many ways can this problem be solved?

23. I am sure that I will prepare everything carefully.

I'm sure that everything will be prepared carefully by me

28. she couldn’t catch his name.

His name couldn't be caught by her

31.Jane is going to buy a new computer.            

A new computer is going to be bought by Jane       

32. He is going to sell his house.               

His house is going to be sold by him

33.Millions of people will visit the museum .    

The museum will be visited by millions of people

35. Nothing will affect the result of the competition.

The result of the competition won't be affected

37. We will force the villagers to work hard

The villagers will be forced to work hard by us

38.They should ask him before giving the decision.        

He should be asked before they give the decision   

40. They have to cancel the meeting.

The meeting has to be cancelled

41. She needs to clean the floor.     

The floor needs to be cleaned

Chào em, em tham khảo nhé!

8. The examiners have to read the passage 3 times.

=> The passage has to be read 3 times by the examiners.

12.They will have to pull down that building.

=> That building will have to be pulled down.

17. You should pay more attention to your study.

=> Your study should be paid more attention to.

18.They can see the valley from the top of this hill.

=> The valley can be seen from the top of this hill.

19.You must wash your hands.

=> Your hands must be washed.

20. Will you post this letter on the way to work?

=> Will this letter be posted on the way to work?

22. How many ways can you solve this problem?

=> How many ways can this problem be solved?

23. I am sure that I will prepare everything carefully.

=> I am sure that everything will be prepared carefully.

28. She couldn’t catch his name.

=> His name couldn't be caught by her.

31.Jane is going to buy a new computer.  

=> A new computer is going to be bought by Jane.                 

32. He is going to sell his house.                

=> His house is going to be sold by him.

33.Millions of people will visit the museum.

=> The museum will be visited by millions of people.    

35. Nothing will affect the result of the competition.

=> The result of the competition will not be affected (by anything).

37. We will force the villagers to work hard.

=> The villagers will be forced to work hard.

38.They should ask him before giving the decision.

=> He should be asked before giving the decision.           

40. They have to cancel the meeting.

=> The meeting has to be cancelled.

41. She needs to clean the floor.         

=> The floor needs cleaning/to be cleaned by her.            

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