a) \(\dfrac{118}{309}>\dfrac{119}{312}\)

b) \(\dfrac{305}{406}< \dfrac{76}{101}\)

Gọi m và c lần lượt là tuổi mẹ và tuổi con năm nay.

Ta có:

m=c+30 (1)

Sau 2 năm ta có:

m+2+c+2=44

=>m+c=40 (2)

Thay (1) vào (2), ta có:

c+30+c=40

=> tuổi con: c=5 tuổi

=> tuổi mẹ m=c+30= 35 tuổi

\(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}< 0\) ( Đk : x\(\ge0\), x khác 4 )

Ta có : 

\(\sqrt{x}\ge0;2>0\)

\(\Rightarrow\sqrt{x}+2>0\)

\(\Rightarrow\sqrt{x}-2< 0\)

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

\(\Leftrightarrow x< 4\)

Kết hợp các điều kiện : x < 4 , x khác 4 ; x \(\ge0\)

\(\Rightarrow0\le x< 4\)

a) Đặt \(P=\dfrac{3+4\sqrt{3}}{\sqrt{6}+\sqrt{2}-\sqrt{5}}\) 

\(P=\dfrac{\left(3+4\sqrt{3}\right)\left(\sqrt{6}+\sqrt{2}+\sqrt{5}\right)}{\left(\sqrt{6}+\sqrt{2}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{2}+\sqrt{5}\right)}\)

Mà \(H=\left(\sqrt{6}+\sqrt{2}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{2}+\sqrt{5}\right)\)

\(H=\left(\sqrt{6}+\sqrt{2}\right)^2-\left(\sqrt{5}\right)^2\)

\(H=8+4\sqrt{3}-5\)

\(H=3+4\sqrt{3}\)

Do đó \(P=\dfrac{\left(3+4\sqrt{3}\right)\left(\sqrt{6}+\sqrt{2}-\sqrt{5}\right)}{3+4\sqrt{3}}\)

\(P=\sqrt{6}+\sqrt{2}+\sqrt{5}\)

b) Đặt \(U=\dfrac{1}{2+\sqrt{5}+2\sqrt{2}+\sqrt{10}}\)

Ta có \(O=2+\sqrt{5}+2\sqrt{2}+10\) 

\(O=\left(2+\sqrt{5}\right)+\sqrt{2}\left(2+\sqrt{5}\right)\)

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

Vậy \(U=\dfrac{1}{\left(2+\sqrt{5}\right)\left(1+\sqrt{2}\right)}\)

\(U=\dfrac{\left(\sqrt{2}-1\right)\left(\sqrt{5}-2\right)}{\left[\left(2+\sqrt{5}\right)\left(\sqrt{5}-2\right)\right]\left[\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)\right]}\)

\(U=\dfrac{\sqrt{10}-2\sqrt{2}-\sqrt{5}+2}{N}\)

Với \(N=\left[\left(2+\sqrt{5}\right)\left(\sqrt{5}-2\right)\right]\left[\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)\right]\)

\(N=\left[\left(\sqrt{5}\right)^2-2^2\right]\left[\left(\sqrt{2}\right)^2-1\right]\)

\(N=\left(5-4\right)\left(2-1\right)\)

\(N=1\)

Do đó \(U=\sqrt{10}-2\sqrt{2}-\sqrt{5}+2\)

    A =          \(\dfrac{1}{2}\) + \(\dfrac{1}{2^2}\)+ \(\dfrac{1}{2^3}\)+ .....+\(\dfrac{1}{2^{98}}\)+\(\dfrac{1}{2^{99}}\)

2xA =    1 +  \(\dfrac{1}{2}\)  + \(\dfrac{1}{2^2}\)+\(\dfrac{1}{2^3}\)+....+\(\dfrac{1}{2^{98}}\)

2A - A =  1 - \(\dfrac{1}{2^{99}}\)

       A =  1 - \(\dfrac{1}{2^{99}}\)

A=1/2+1/2^2+1/2^3+...+1/2^99

Dãy số chia hết cho 3 nhỏ hơn 123 là :

      3, 6, 9, . . ., 117,120

Có tất cả số số hạng là:

    ( 120 - 3) : 3 + 1 = 40 ( số hạng )

Dãy số trên có tổng là:

          ( 120+3) x 40 : 2 = 2460

 Vậy tổng các số chia hết cho 3 nhỏ hơn 123 là : 2460

.

số số hạng của dãy số trên là: (999-1)/1+1=999

tổng các số trên là : (999+1).999/2=49950

1) I was a student 2 years ago.
2) He was a doctor two years ago. 
3) They were farmers last year. 
4) Lan and Ba were nurses last year. 
5) It wasn't cold yesterday. 
6) She wasn't a pupil last week. 
7) This hat wasn't new yesterday. 
8) My parents weren't teachers two years ago. 
9) He wasn't a mechanic last Monday. 
10) Was he an engineer yesterday. No, he wasn't 
11) Was it hot last week? 
12) The windows were open last Monday.
13) Was you a teacher two years ago? Yes, I was. 
14) Where was Nam from yesterday? 
15) Why was he unhappy last Tuesday? 

1) I remembered your trip to Nha Trang two years ago.
2) Ba wore the cap all day yesterday. 
3) I ate a lot of fish yesterday. 
4) Her aunt took her to see Cham Temple last year. 
5) Tuan had a new bike yesterday. 
6) Didn't she buy a new ruler yesterday? 
7) He didn't talk with his parents about his vacation in Da Lat last year. 
8) Didn't they come to school yesterday? 
9) The window didn't close yesterday.
10) We didn't return at home at 7 pm last Monday.
11) She didn't eat fish and crab yesterday.
12) Lan didn't go to Ho Chi Minh city two years ago. 
13) My parents didn't take to Vung Tau last week. 
14)We didn't have a lot of friends in Ha Noi.
15) Were Lan and Hoa your school two years ago?
16) What did they play last week?
17) What did Hoa try on yesterday? 
18) Who told to about the film on TV last Monday? 
19) Where did they stop on their way back last Sunday?
20) What did the student wear at school two years ago?
21) Where did you put the cake yesterday?
22) What time did you leave home for school yesterday? 
23) What did Ba receive from Liz last week? 
24) How long did he do this hat yesterday?
25) What time did you go to bed last night?
26) Did You go to Dalat for last tet vacation?
27) Did he have a lot of friends in Ho Chi Minh city 3 years ago? 
28) Did his uncle take him to see Tri Nguyen aquarium last week?
29) Did Liz buy a lot of souvenirs yesterday? 
30) Did they put the fish in the big bag last Sunday? 
31) Did they eat meat in her meals in Vung Tau yesterday? 
32) Did I wear the cap with a dolphin on it yesterday?
33) Did Liz teach Ba some English last week? 
34) Did Bad and Tan remember their trip to Nha Trang last month?
35) Did Nam return to Ha Noi last week?

Không rõ đề nên làm 2 trường hợp 

+) \(\sqrt{x}+\dfrac{2}{\sqrt{x}}-2< 0\) ( x > 0 )

\(\Leftrightarrow\dfrac{x+2-2\sqrt{x}}{\sqrt{x}}< 0\)

\(\Rightarrow x-2\sqrt{x}+2< 0\)

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

\(\Leftrightarrow\left(\sqrt{x}-1\right)^2+1< 0\)( vô lí ) 

+) \(\sqrt{x}+\dfrac{2}{\sqrt{x}-2}< 0\)

\(\Leftrightarrow\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)+2}{\sqrt{x}-2}< 0\) ( x khác 4 , x \(\ge\) 0)

\(\Leftrightarrow\dfrac{x-2\sqrt{x}+2}{\sqrt{x}-2}< 0\)

\(\Leftrightarrow\sqrt{x}-2< 0\) ( do ở ý trên đã cm được tử > 0

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

\(\Leftrightarrow x< 4\)

Kết hợp các điều kiện

\(\Rightarrow0\le x< 4\)

Bạn chụp lại đầy đủ giúp mình ạ!
Để mình giải cho ạ!

1. go camping

2. go to a disco

3. take photos

4. swimming

5. have an ice cream