\(a^3+b^3=\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}-\dfrac{4\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}\)

\(=\sqrt{6}-\sqrt{2}-\dfrac{4\left(\sqrt{6}-\sqrt{2}\right)}{4}=0\)

\(\Rightarrow a=-b\Rightarrow a^5+b^5=0\)

`2)B=(sqrtx+1)/(x-1)-(x+2)/(xsqrtx-1)-(sqrtx+1)/(x+sqrtx+1)(x>0,x ne 1)`

`=(sqrtx+1)/(x-1)-(x+2)/(xsqrtx-1)-(x-1)/(xsqrtx-1)`

`=(sqrtx+1)/(x-1)-(x+2+x-1)/(xsqrtx-1)`

`=(sqrtx+1)/(x-1)-(2x+1)/(xsqrtx-1)`

`=((sqrtx+1)(x+sqrtx+1)-(2x+1)(sqrtx+1))/((x-1)(x-sqrtx+1))`

`=(xsqrtx+2x+2sqrtx+1-2xsqrtx-2x-sqrtx-1)/((x-1)(x-sqrtx+1))`

`=(-xsqrtx+sqrtx)/((x-1)(x-sqrtx+1))`

`=(-sqrtx(x-1))/((x-1)(x-sqrtx+1))`

`=-sqrtx/(x-sqrtx+1)`

Cách khác:

2) Ta có: \(B=\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)

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

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

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

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

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

2b) \(\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)

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

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

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

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

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

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

`3b)\sqrt{25x-25}-15/2\sqrt{(x-2)/9}=6+3/2\sqrt{x-1}`

ĐK:`x>=1`

`pt<=>sqrt{25(x-1)}-15/2*1/3sqrt{x-1}-3/2sqrt{x-1}=6`

`<=>5sqrt{x-1}-5/2sqrt{x-1}-3/2sqrt{x-1}=6`

`<=>5sqrt{x-1}-4sqrt{x-1}=6`

`<=>sqrt{x-1}=6`

`<=>x-1=36`

`<=>x=37(tmddk)`

Vậy `S={37}`

3b) \(\sqrt{25x-25}-\dfrac{15}{2}\sqrt{\dfrac{x-1}{9}}=6+\dfrac{3}{2}\sqrt{x-1}\left(x\ge1\right)\)

\(\Leftrightarrow\sqrt{25\left(x-1\right)}-\dfrac{15}{2}\sqrt{\dfrac{1}{9}.\left(x-1\right)}-\dfrac{3}{2}\sqrt{x-1}=6\)

\(\Leftrightarrow5\sqrt{x-1}-\dfrac{15}{2}.\dfrac{1}{3}\sqrt{x-1}-\dfrac{3}{2}\sqrt{x-1}=6\)

\(\Leftrightarrow5\sqrt{x-1}-\dfrac{5}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{x-1}=6\)

\(\Leftrightarrow\sqrt{x-1}=6\Rightarrow x-1=36\Rightarrow x=37\)

Bài 3: 

c) ĐKXĐ: \(x\ge0\)

Ta có: \(\sqrt{4+5\sqrt{x}}=3\)

\(\Leftrightarrow5\sqrt{x}+4=9\)

\(\Leftrightarrow5\sqrt{x}=5\)

\(\Leftrightarrow x=1\)

Vậy: S={1}

d) Ta có: \(x-\sqrt{4x-20}=20\)

\(\Leftrightarrow\sqrt{4x-20}=x-20\)

\(\Leftrightarrow\left(x-20\right)^2=4x-20\)

\(\Leftrightarrow x^2-40x+400-4x+20=0\)

\(\Leftrightarrow x^2-44x+420=0\)

\(\Delta=\left(-44\right)^2-4\cdot1\cdot420=256\)

Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{44-16}{2}=\dfrac{28}{2}=14\\x_2=\dfrac{44+16}{2}=\dfrac{60}{2}=30\end{matrix}\right.\)

Vậy: S={14;30}

Ta có:x²+y²=25➝(x+y)²-2xy=25➝(x+y)²=1➝x+y=1.Đến đây bạn tự làm.

a: =>x=y+11

xy=60

\(\Leftrightarrow y^2+11y-60=0\)

\(\Leftrightarrow\left(y+15\right)\left(y-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}y=-15\\y=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=15\end{matrix}\right.\)

a)

$Mg + H_2SO_4 \to MgSO_4 + H_2$
$Mg + 2H_2SO_{4_{đặc}} \to MgSO_4 + SO_2 + 2H_2O$
$Cu + 2H_2SO_{4_{đặc}} \to CuSO_4 + SO_2 + 2H_2O$

Theo PTHH : 

n Mg = n H2 = 0,448/22,4 = 0,02(mol)

Mặt khác : n SO2 = 2,688/22,4 =0,12(mol)

4m gam X chứa 4n Cu và 0,02.4 = 0,08 mol Mg

Theo PTHH : n SO2 = n Cu + n Mg

=> n Cu = (0,12- 0 ,08)/4 = 0,01(mol)

Suy ra:  m = 0,01.64 + 0,02.24 = 1,12(gam)

b) $SO_2 + Br_2 + 2H_2O \to 2HBr + H_2SO_4$

n Br2 = n SO2 = 0,12(mol)

=> V dd Brom  = 0,12/0,02 = 6(lít)

a.

ĐKXĐ: \(-3\le x\le\dfrac{3}{2}\)

Ta có:

\(4\sqrt{x+3}=2.2\sqrt{x+3}\le2^2+x+3=x+7\)

\(2\sqrt{3-2x}=2.1.\sqrt{3-2x}\le1^2+3-2x=4-2x\)

Do đó:

\(x+4\sqrt{x+3}+2\sqrt{3-2x}\le x+x+7+4-2x=11\)

Đẳng thức xảy ra khi và chỉ khi:

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

Vậy pt có nghiệm duy nhất \(x=1\)

b.

ĐKXĐ: \(x\ge-\dfrac{3}{2}\)

\(x^2+4x+5-2\sqrt{2x+3}=0\)

\(\Leftrightarrow\left(x^2+2x+1\right)+\left(2x+3-2\sqrt{2x+3}+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)^2+\left(\sqrt{2x+3}-1\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+1=0\\\sqrt{2x+3}-1=0\end{matrix}\right.\)

\(\Leftrightarrow x=-1\)

Vậy pt có nghiệm duy nhất \(x=-1\)

Cách 2 câu a:

\(\Leftrightarrow11-x-4\sqrt{x+3}-2\sqrt{3-2x}=0\)

\(\Leftrightarrow\left(x+3-4\sqrt{x+3}+4\right)+\left(3-2x-2\sqrt{3-2x}+1\right)=0\)

\(\Leftrightarrow\left(\sqrt{x+3}-2\right)^2+\left(\sqrt{3-2x}-1\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+3}-2=0\\\sqrt{3-2x}-1=0\end{matrix}\right.\)

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

\(\Leftrightarrow x=1\)

1) The student is from Vietnam. She sits next to me.

->The student who sits next to me is from Vietnam
2) I thanked the woman. This woman had helped me.

->I thanked the woman who had helped me
3) The professor is excellent. I’m taking his course.

->The professor whose course I'm taking is excellent
4) The man is my father. I respect his opinions most.

->The man whose opinions I respect most is my father
5) She is the most intelligent woman. I have never met this woman.

->She is the most intelligent woman that I have ever met
6) Do you know the music ? It is being played on the radio.

->Do you know the music which is being played on the radio
7) I recently went back to Paris. It is still as beautiful as a pearl

->I recently went back to Paris which is still as beautiful as a pearl
8) That man is an artist. I don’t remember the man’s name.

->That man is an artist whose name I don't remember
9)  That car belongs to Dr. Clark. Its engine is very good.

->That car whose engine is very good belongs to Dr. Clark
10)  This is Mrs. Jones. Her son won the championship.

->This is Mrs. Jones whose son won the championship
11)  There is a No Parking sign. I don’t take notice of it.

->There is a No Parking sign of which I don't take notice
12)  His letter is full of interesting news. I received it two days ago.

->His letter which I received two days ago is full of interesting new
13)  The book is about Africa. It has some wonderful pictures.

->The book which has some beautiful pictures is about Africa
14)  My mother still goes in for sports. She is over 45.

->My mother who is over 45 still goes in for sports
15)  The tables are old. They are in the living room.

->The tables which are in the living room are old 
16)  The book was torn. I gave it to him. 

->The book which I gave to him was torn
17)  Last month my father bought me a book. It was very expensive. 

->Last month my father bought me a book which was very expensive
18)  The knife was dull. She used it to cut bread.  

->The knife which she used to cut bread was dull
19)  Do you see these cars? They have just passed by. 

=>Do you see these cars which have just passed by?
20)  Have you ever ridden the horse? She bought it in Tu Xuyen. 

->Have you ever ridden the horse which she bought in Tu Xuyen?
21) The computer was bought last month. It belonged to my sister.

->The computer which was bought last month belonged to my sister 
22) The house was in bad condition. They built it three centuries ago.

The house which was built three centuries ago was in bad condition
23) The man gave me some screwdrivers(cái tua vít). They were not in good condition. 

->The man gave me some screwdrivers that were not in good condition
24) They showed me the photos. They took them during the trip in Japan. 

-> They showed me the photos which were taken by them during the trip   in Japan
25) Do you know the man? He is talking to the principal. 

->Do you know the man who is talking to the principal?
26) The man is standing in front of the house. He is complaining about the waste. 

->The man who is standing in front of my house is complaining about the waste
27) All the people have disliked him. I have never met them.

->All the people whom I have never met have disliked him
28) The book is new. I have just bought it.

->The book which I have just bought is new
29) Anybody may leave. They are tired.

->Anybody who are tired may leave
30)  The dictionary was given by my sister. She has just returned from England. 

->The dictionary was given by my sister who has just returned from England
31)  That is everything. She needs them for her camping trip. 

->That is everything       that she needs for her camping trip
32)  There’s the man. His wallet was stolen.

->There's the man whose wallet was stolen
33) There are a few things. We can do them.

->There are a few things that we can do
34) I met the woman. Her husband is the president of the cor­poration.

-> I met the woman whose husband is the president of the corporation
35)  I come from a country. Its history goes back thousands of years.

I come from a country whose history goes back thousands of years
36) This is the pupil. You might want to make friends with him. 

->The is the pupil with whom you might want to make friends
37) The professor is excellent. I am taking her course.

->The professor whose course I am taking is excellent
38) Mark Twain is an author. You like his books best.

->Mark Twain is an author whose books you like best

không sao bạn ơi có sai mình cũng chấp nhận nha <3