Bài 1:

c) \(C=\dfrac{5}{\sqrt{7}+\sqrt{2}} - \sqrt{8-2\sqrt{7}} + \sqrt{2} \)

⇔ \(C=\dfrac{5}{\sqrt{7}+\sqrt{2}} - \sqrt{(\sqrt{7})^2 - 2\sqrt{7}+1} + \sqrt{2} \)

⇔ \(C=\dfrac{5}{\sqrt{7}+\sqrt{2}} - \sqrt{(\sqrt{7}-1)^2} + \sqrt{2} \)do 

⇔ \(C=\dfrac{5}{\sqrt{7}+\sqrt{2}} - |\sqrt{7}-1| + \sqrt{2} \)

⇔ \(C=\dfrac{5}{\sqrt{7}+\sqrt{2}} - \sqrt{7}+1 + \sqrt{2} \)   (do \(\sqrt{7} > 1 \))

⇔ \(C=\dfrac{5}{\sqrt{7}+\sqrt{2}} - (\sqrt{7} - \sqrt{2}) +1 \)

⇔ \(C=\dfrac{5-(\sqrt{7} - \sqrt{2})(\sqrt{7}+\sqrt{2})}{\sqrt{7}+\sqrt{2}} +1 \)

⇔ \(C=\dfrac{5-7+2}{\sqrt{7}+\sqrt{2}} +1 =\dfrac{0}{\sqrt{7}+\sqrt{2}} +1 \)

⇔ \(C = 0 + 1 = 1\)

Vậy \(C=1\)

Bài 3: 

c) Ta có: \(M=\dfrac{Q}{P} \)

⇔ \(M=\dfrac{\dfrac{\sqrt{x}}{\sqrt{x}-2}}{\dfrac{\sqrt{x}+5}{\sqrt{x}-2} } \)

⇔ \(M=\dfrac{\sqrt{x}}{\sqrt{x}+5} \)

Mà:  \(M<\dfrac{1}{2} \) ⇔ \(\dfrac{\sqrt{x}}{\sqrt{x}+5} <\dfrac{1}{2} \)

⇒ \(2\sqrt{x} < \sqrt{x}+5 \) (nhân 2 vế với \(2.(\sqrt{x} +5) >0\))

⇔ \(\sqrt{x}<5 \) ⇔ \(x<25\)

Kết hợp điều kiện ban đầu, ta đc:

Vậy khi \(0≤x<25\) và \(x≠4\) thì \(M=\dfrac{Q}{P} < \dfrac{1}{2} \)

Bài 1: 

a: \(A=\sqrt{18}-2\sqrt{50}+3\sqrt{8}\)

\(=3\sqrt{2}-10\sqrt{2}+6\sqrt{2}\)

\(=-\sqrt{2}\)

BÀi 3:

a: Thay \(x=7-4\sqrt3=\left(2-\sqrt3\right)^2\) vào Q, ta được:

\(Q=\frac{\sqrt{\left(2-\sqrt3\right)^2}+1}{\sqrt{\left(2-\sqrt3\right)^2}+2}=\frac{2-\sqrt3+1}{2-\sqrt3+2}=\frac{3-\sqrt3}{4-\sqrt3}\)

\(=\frac{\left(3-\sqrt3\right)\left(4+\sqrt3\right)}{\left(4-\sqrt3\right)\left(4+\sqrt3\right)}=\frac{12+3\sqrt3-4\sqrt3-3}{16-3}=\frac{9-\sqrt3}{13}\)

b: \(P=\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{1}{1-\sqrt{x}}-\frac{2\sqrt{x}}{x-1}\)

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

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

\(M=P\cdot Q\)

\(=\frac{\sqrt{x}-1}{\sqrt{x}+1}\cdot\frac{\sqrt{x}+1}{\sqrt{x}+2}=\frac{\sqrt{x}-1}{\sqrt{x}+2}\)

c: \(M<-\frac13\)

=>\(M+\frac13<0\)

=>\(\frac{\sqrt{x}-1}{\sqrt{x}+2}+\frac13<0\)

=>\(\frac{3\sqrt{x}-3+\sqrt{x}+2}{3\left(\sqrt{x}+2\right)}<0\)

=>\(4\sqrt{x}-1<0\)

=>\(4\sqrt{x}<1\)

=>\(\sqrt{x}<\frac14\)

=>0<=x<1/16

a: Bảng giá trị:

Vẽ đồ thị

Phương trình hoành độ giao điểm là:

2x+1=-x+3

=>2x+x=3-1

=>3x=2

=>\(x=\frac23\)

Khi x=2/3 thì \(y=-x+3=-\frac23+3=\frac73\)

Vậy: Tọa độ giao điểm là A(2/3;7/3)

b: Bảng giá trị:

Vẽ đồ thị:

Phương trình hoành độ giao điểm là:

\(x-1=-\frac12x+2\)

=>\(x+\frac12x=2+1\)

=>1,5x=3

=>x=2

Khi x=2 thì y=2-1=1

Vậy: Tọa độ giao điểm là B(2;1)

c: Bảng giá trị:

Vẽ đồ thị:

Vì a=a'(2=2) và b<>b'(-3<>2)

nên (D)//(D')

=>(D) và (D') không có giao điểm

d: Bảng giá trị:

Vẽ đồ thị:

Phương trình hoành độ giao điểm là:

3x+1=-2x+3

=>5x=2

=>\(x=\frac25\)

Khi x=2/5 thì \(y=-2x+3=-2\cdot\frac25+3=3-\frac45=\frac{11}{5}\)

Vậy: Tọa độ giao điểm là D(2/5;11/5)

Bài 5: 

1. There are a few students taking part in the event     

→ There aren't many students taking part in the event.

2. If he doesn't work hard, he will lose his job     

→ Unless he works hard, he will lose his job.

3. Let's write about the three Rs ?         

→ Why  don't we write about the three Rs?

4. Learning about recyking is fun           

→ It's fun to learn about recycling.

5. It's not good to throw old clothes away               

→ You  shouldn't throw old clothes away

Xếp từ thành câu

Bài 1

1. they / to / movies / do / how / go / the / often ?   

→ How often do they go to the movies?

2. your eyes / swimming / should / when  goggles / you / you / go / wear / to protect

→ When you go swimming, you should wear goggles to protect your eyes.

3. usually / his  / swimming / with / friends / he / goes       

→ He usually goes swimming with his friends.

4. go / do / weekend / on / always / fishing / parents / their ?   

→ Do their parents always go fishing on the weekend?

5. camping / they / go / do / sometimes

→  Sometimes they go camping.

6. what / TV / you / do / on / sports / watch?

→ What sports do you watch on TV?

Bài 2

1. Our / important / an / sports and games / in play / lives / part       

→ Sports and games play an important part in our lives.       

2. players / how / match / there / in / many / are / football / a ?   

→ How many players are there in a football match?

3. by / she / to keep / every day / tries / fit / jogging 

→ She tries to keep fit by jogging every day.

4. yesterday / who / play / football / you / did / with ?

→ Who did you play football with yesterday?

5. sports / building / physical and strength / necessary / are / for

→ Sports are necessary for building physical strength.

6. to switch / before / go / don't / the TV / off / you / forget / to bed

→ Don't forget to switch off the TV before you go to bed.

7. Sunday / I / usually / friends / swimming / on / go / mornings / with / my

→ On Sunday mornings, I usually go swimming with my friends.

8. match / you / on / the / did / television / last night / watch / basketball / the ?

→ Did you watch the basketball match on television last night? 

Bài đâu anh?

Ýe^^ câu hỏi đâu bro