Hiền Thương
Giới thiệu về bản thân
\(x^3+2x-3=0\)
\(\Leftrightarrow x^3-x+3x-3=0\)
\(\Leftrightarrow x\left(x^2-1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow x\left(x+1\right)\left(x-1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x\left(x+1\right)+3\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x+3\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(x^2+x+\dfrac{1}{4}\right)+3-\dfrac{1}{4}\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}\right]=0\) (*)
Vì \(\left(x+\dfrac{1}{2}\right)^2\ge0\forall x\Rightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}>0\forall x\) (**)
Từ (*);(**) => \(x-1=0\) =>x=1
Vậy x=1
Gọi số học sinh 6A,6B,6C,6D lần lượt lượt là: x,y,z,k (x,y,z,k\(\in\) N*)
Theo bài ra ta có:
Số học sinh 6A,6B,6C,6D tỉ lệ với 9;8;6;5
=> \(\dfrac{x}{9}=\dfrac{y}{8}=\dfrac{z}{6}=\dfrac{k}{5}\)
Và y-z = 10
Áp dụng tính chất dãy tỉ số bằng nhau,ta có :
\(\dfrac{x}{9}=\dfrac{y}{8}=\dfrac{z}{6}=\dfrac{k}{5}=\dfrac{y-z}{8-6}=\dfrac{10}{2}=5\)
=> \(\left\{{}\begin{matrix}x=5\cdot9\\y=5\cdot8\\z=5\cdot6\\k=5\cdot5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=45\\y=40\\z=30\\k=25\end{matrix}\right.\)
Vậy số học sinh 6A ,6N,6C,6D lần lượt là 45,40,30,25 học sinh
1. John tennis once or twice a week.
A. is playing usually B. is usually playing
C. usually plays D. plays usually
2. Tom his hand when he was cooking dinner.
A. burnt B. was burning C. has burnt D. had burnt
3. Jim is away on holiday. He to Spain.
A. is gone B. have been C. has been D. was
4. Everything is going well. We any problems so far.
A. didn't have B. don't have C. haven't had D. hadn't had
5. Jane just a few minutes ago.
A. left B. has left C. leaves D. had left
6. Timson 13 films and I think the latest is the best.
A. made B. had made C. has made D. was making
A. Did you see B. Have you seen C. Do you see D. Are you seeing
8. When I was a child, I the violin.
A. was playing B. am playing C. played D. play
9. He for the national team in 65 matches so far.
A. has played B. has been played C. played D. is playing
10. I'm busy at the moment. I on the computer.
A. work B. worked C. am working D. working
11. When I looked round the door, the baby quietly.
A. is sleeping B. slept C. was sleeping D. were sleeping
12. Robert ill for three weeks. He is still in hospital.
A. had been B. has been C. is D. was
13. I'm very tired. I over four hundred miles today.
A. drive B. am driving C. have drived D. have driven
14. What time to work this morning?
A. did you get B. are you getting C. have you got D. do you get
15. When I this man, he was running away
A. see B. was seeing C. saw D. had seen
16. As soon as Martina saw the fire, she the fire department.
A. was telephoning B. telephoned
C. had telephoned D. has telephoned
17. Every time Parkas sees a movie made in India, he homesick.
A. will have left B. felt C. feels D. is feeling
18. After the race , the celebration began.
A. had been won B. is won C. will be won D. has been won
19. The earth on the sun for its heat and light.
A. is depended B. depends C. is depending D. has depended
20. When I entered the room, everyone
A. has been dancing B. was dancing C. had danced D. danced
21. Iwas very tired because I all the day.
A. have worked B. have been working
C. had worked D. had been working
22. How long able to drive? - Since 1990.
A. could you B. have you been C. were you D. are you
23. When she the noise, she down to the kitchen and on the lights.
A. hears; goes; turns B. heard; went; turned
C. heard; was going; turned D. had heard; went; had turned
24. Jane and I school in 1987.
A. finish B. have finished C. finishes D. finished
A. I was watching TV. B. I watched TV. C. I am watching TV D. I have watched TV.
27.Everyday, my sister the floor.
A. usually clean B. cleans usually C. usually cleaned D. usually cleans
28. After they their breakfast, they shopping yesterday.
A. have; go B. had had; go C. had; had gone D. had had; went
29. Father his pipe while mother a magazine.
A. smoked; read B. was smoking; was reading
C. had smoked; read D. smoking; reading
30. When we came to the stadium, the match
1. My clothes are not in the room. They (just take) have just taken them away.
2. This is the most beautiful place I (ever visit) have ever visited
3. We are very tired. We (walk) have walked for three hours.
4. I have seen (see) that film several times because I like it.
5. Up to now, the teacher (give) has given our class 5 tests.
6. Please be quiet! I (work) …am working……………
7. Mary (come) comes from London.
8. Sometimes I (get) get up before the sun (rise) rises .
9. She (ask) asks me to tell about him several times.
10. Mr Jackson (paint) has painted his house since last month.
11. How long you (wait) have you waited for me? - Just a few minutes.
12. He often (say) says OK when he (talk) talks with the guests.
13. Tom (not come) won't come here tomorrow.
14. Listen! The bird (sing) …is singing……………
15. Someone (cut) has cut down all the trees in the garden.
16. Some animals (not eat) don't eat during winter.
17. Hurry up! The train (come) is coming .
18. Where are you now? - I'm upstairs. I (have) am having a bath.
Từ ƯCLN(a,b)=2
=> \(\left\{{}\begin{matrix}a=2m\\b=2n\end{matrix}\right.\) (ƯCLN(m,n)=1 hay m,n nguyên tố cùng nhau)
Mà 2a+3b = 18
<=> 2.2m + 3.2n = 18
<=> 2( 2m+3n) =18
=> 2m+3n = 9
Vì m,n nguyên tố cùng nhau nên ta có bảng
| m | 3 |
| n | 1 |
| a | 6 |
| b | 2 |
Vậy a=6;b=2
Tổng của 3 số lẻ liên tiếp ở trên là :
47*3 = 141
Gọi 3 số lẻ liên tiếp lần lượt là :n,n+2,n+4
Theo bài ra ta có :
n +(n+2) +(n+4) = 141
3n + 6 =141
=> 3n=141-6
3n=135
=> n= 45
Vậy 3 số lẻ liên tiếp lần lượt là 45,47,49
a, \(\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}+\dfrac{3}{14\cdot17}+....+\dfrac{3}{92\cdot95}\)
\(=\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}+...+\dfrac{1}{92}-\dfrac{1}{95}\)
\(=\dfrac{1}{8}-\dfrac{1}{95}\)
\(=\dfrac{87}{760}\)
b, \(\dfrac{5}{7\cdot12}+\dfrac{5}{12\cdot17}+\dfrac{5}{17\cdot22}+...+\dfrac{5}{92\cdot97}\)
\(=\dfrac{1}{7}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{22}+....+\dfrac{1}{92}-\dfrac{1}{97}\)
\(=\dfrac{1}{7}-\dfrac{1}{97}\)
\(=\dfrac{90}{679}\)
c, \(\dfrac{3}{1\cdot2}+\dfrac{3}{2\cdot3}+\dfrac{3}{3\cdot4}+...+\dfrac{3}{99\cdot100}\)
\(=3\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\right)\)
\(=3\cdot\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(=3\left(\dfrac{1}{1}-\dfrac{1}{100}\right)\)
\(=3\cdot\dfrac{99}{100}=\dfrac{297}{100}\)
\(n+2⋮n-1\)
<=> (n-1) +3 \(⋮\) n-1
Vì n-1\(⋮\) n-1
Để n+2\(⋮\) n-1 => 3\(⋮\) n-1 hay n-1\(\inƯ\left(3\right)=\left\{1;3;-1;-3\right\}\)
=> n \(\in\left\{2;4;0;-2\right\}\)
Gọi số cần tìm là x(x\(\in\)N*)
Vì khi chia cho 3,4 và 5 thì số dư tương ứng là 2,3,4
\(\left\{{}\begin{matrix}x+1⋮3\\x+1⋮4\\x+1⋮5\end{matrix}\right.\) \(\Rightarrow x+1\in BC\left(3;4;5\right)\)
Ta có : 3=3 ; 4=22; 5=5
=> BCNN(3;4;5=22 *3*5 = 60
BC(3;4;5)=B(60)={0;60;120;180;240;300;...}
<=> x+1 \(\in\) {0;60;120;180;...}
=> x\(\in\) {59;119;179;,,,,}
Vì x là số nhỏ nhất và chia hết cho 7
=> x = 119