Đáp án:
Giải thích các bước giải:
Có: `1/2 ( a - b )^2 + 1/2 ( a - 1 )^2 + 1/2 ( b - 1 )^2 ≥ 0` ( với mọi `a , b` )
`<=> 1/2 ( a^2 - 2ab + b^2 ) + 1/2 ( a^2 - 2a + 1 ) + 1/2 ( b^2 - 2b + 1 ) ≥ 0`
`<=> 1/2 a^2 - ab + 1/2 b^2 + 1/2 a^2 - a + 1/2 + 1/2 b^2 - b + 1/2 ≥ 0`
`<=> ( 1/2 a^2 + 1/2 a^2 ) + ( 1/2 b^2 + 1/2 b^2 ) + ( 1/2 + 1/2 ) ≥ ab + a + b`
`<=> a^2 + b^2 + 1 ≥ ab + a + b ( đpcm )`
Áp dụng bất đẳng thức: $x^{2}$ + $y^{2}$ $\geq$ 2xy (vì $(x-y)^{2}$ $\geq$ 0 với mọi x,y)
$a^{2}$ + $b^{2}$ $\geq$ 2ab$a^{2}$ + 1 $\geq$ 2a$b^{2}$ + 1$\geq$ 2bCộng vế với vế của các bât đẳng thức trên ta có:2($a^{2}$ + $b^{2}$ + 1) $\geq$ 2(ab+a+b)<=> $a^{2}$ + $b^{2}$ +1$\geq$ ab+a+b
Rewrite these following sentences without changing their meanings: 1. John smoked a lot a year ago, but now he doesn't smoke any more. —> John used__________________ 2. It's time for you to go to school. —> It's time you_________________ 3. How long is it since you saw Tom? —> When______________________ 4. Please keep silent in the classroom. —> I'd rather____________________ 5. He has to work hard for the exam. —> He wishes___________________ 6. We need to clean all the plates after dinner. —> We wish____________________ 7. I don't like you to come to class last. —> I'd rather you_________________ 8. What a pity! He can't come here. —> I wish______________________ 9. They often went to Vung Tau at weekends. —> They used___________________ 10. She isn't here. —> She wishes__________________
Tìm số tự nhiên x 84 - 2(x+1)= 22
Người thứ nhất đi theo chiều từ A đến B với vận tốc 25km/giờ. Cùng lúc tại B,người thứ hai cũng khởi hành và đi cùng chiều với người thứ nhất với vận tốc 20km/giờ. Biết rằng khoảng cách AB = 10km.Hỏi sau bao lâu hai người gặp nhau?
Cho tam giác ABC là tam giác vuông tại A,có AH là đường cao.Gọi M và N lần lượt là hình chiếu của H trên AB,AC.Chứng minh rằng: 1,Tam giác AHB đồng dạng với tam giác CAB 2,AM.AB=AN.AC Vẽ hình giúp mình và giải giúp mình với
Cậu gì đó cute trước màn ơi Cậu có thể giải hộ tớ bài này đc ko Cảm ơn cậu :333
thế nào là anion gốc axit trong muối không có và có tính oxi hoá. lấy ví dụ
Giúp mình với mn ơi mình cần gấp Cảm ơn trước
EXERCISE1: present simple and present continuous Put the verb in the correct form, present continuous or present simple 1. Let’s go out. It______________________ (not/rain) now. 2. Julia is very good at languages. She ___________________ (speak) four languages very well. 3. Hurry up! Everybody____________________ (wait) for you. 4. “_____________________ (you/listen) to the radio?” “No, you can turn it off.” 5. “_____________________ (you/ listen) to the radio every day?” “No, just occasionally” 6. Look at the river. It ____________________ (flow) very fast today- much faster than usual. 7. We usually ______________________ (grow) vegetables in our garden but this year we __________________ (not/grow) any. 8. “How is your English?” “Not bad. It__________________________ (improve) slowly.” 9. Ron is in London at the moment. He __________________________ (stay) at the Park Hotel. He _________________ (always/ stay) there when he’s in London. 10. Can we stop walking soon? I _______________________ (start) to feel tired. 11. A: What __________________ (you/do)? B: I ______________ (write) to my parents. I ________________ (write) to them every weekend. 12. A: Look, it ______________ (snow). B: It’s beautiful! This is the first time I’ve ever seen snow, it _____________ (not snow) in my country. 13. A: Oh, that’s Adrian. He’s new here. B: Really? Where ________________ (he/live)? ______________ (you/know)? A: Yes. He ____________ (live) in Milan, but now he ____________ (stay) with his aunt on Shirley Road. 14. A: What time _________________ (you/ usually/ finish) work? Normally I ____________ (finish) work at 5 o’clock, but this week I __________ (work) until six to earn a bit more money. 15. A: How _________________ (you/ travel) to work? B: I haven’t got a car at the moment, so I ____________ (go) to work on the bus this week. Usually I _________________ (drive) to work. 16. A: I think we’re going the wrong way. B: I don’t think so. The sun ________________ (rise) in the east, remember. It’s behind us, so we _______________ (travel) west. 17. A: _______________ (you/look) for someone? B: Yes, I ______________(need) to speak Neil. Is he in? A: Yes, but I _____________ (think) he’s busy. He ______________ (talk) to ther boss at the moment. 18. A: I _________________ (want) a new computer. I ________________ (save) up to buy one. B: But computers ________________ (cost) so much money. What’s wrong with the one we’ve got? A: It ___________________ (get) out of date now. 19. A: Your new dress ________________ (look) very nice. B: Thank you. The trouble is it _____________ (not/fit) properly. I _____________ (not/know) why I bought them, really. 20. A: What ________________ (you/do)? B: I ______________ (taste) the sauce. It ___________________ (taste) too salty.
Phân tích đa thức thành nhân tử: 4x^4- 21x^2+1
!!! Use the correct preposition and gerund (V-ing) !!! ~~develop, ride, select, threaten, join, sit, kick, give, deal, read, choose, be, criticize, shout, jog, become, make, be, speak, swim, teach, call, paint, go.~~ 1.He complained ___ me ___ ___ suspected by her. 2.They’ve just taken ___ ___ as they want to improve their health. 3.Does Jack interfere with ___ ___ and ___ Jim? 4.We are ___ ___ ___ ill when we are not here. 5. am not well prepared ___ ___ for the job this time. 6.He went ___ ___ because he is very good at it. 7.He is just given ___ ___ the theory. It is, in fact, impossible to do such a thing. 8.Do you feel ___ ___ a bike on such a fine day? 9.There is no point ___ ___ him at this hour. 10. Is it worth ___ to their wedding with a present?
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