Áp dụng BĐT Cauchy cho các số dương, ta có:
`a+b+c\ge 3\root{3}{abc}`
`1/a+1/b+1/c\ge 3\root{3}{1/{abc}}`
Nhân vế với vế của 2 BĐT trên, ta được:
`(a+b+c)(1/a+1/b+1/c)\ge 9\root{3}{abc. 1/{abc}}=9`
Đẳng thức xảy ra `<=>a=b=c`
Đáp án:
`(a+b+c)(1/a+1/b+1/c)>=9`
`<=>1+a/b+a/c+b/a+1+b/c+c/a+c/b+1>=9`
`<=>3+a/b+a/c+b/a+b/c+c/a+c/b>=9`
`<=>a/b+a/c+b/a+b/c+c/a+c/b-6>=0`
`<=>a/b-2+b/a+b/c-2+c/b+c/a-2+a/c>=0`
`<=>(\sqrt{a/b}-\sqrt{b/a})^2+(\sqrt{b/c}-\sqrt{c/b})^2+(\sqrt{c/a}-\sqrt{a/c})^2>=0` đúng `AAa,b,c>0`
Dấu "=" xảy ra khi `a=b=c`.
tạo 5 cái logo "5h3t6" đẹp giúp mik nhé mik cảm ơn trc
Xác định thành phần chính, thành phần phụ trong câu sau:(1) Trên cánh đồng phì nhiêu chạy dài theo con sông Hậu, đàn cò trắng và đàn vịt trời đang bay lươn (2) Từ ngày đầu mới mở cổng trường, chị tính, chị của tôi, đã có mặt
Ai giúp em câu 3 được không ạ ;-;. Em cảm ơn nhiều ạ^^
phụ mình nha, cảm onn nhiềuuuuu
Giải hộ mình với ạ, mình cảm ơn
Viết chữ Bảo nka Calli hay chữ thường cx đc nka:33
1. If you don’t practice harder, you will lose in the next game. => Unless ……………………………………………………………….. 2. If Nam doesn’t speak English everyday, he will easily forget how to use it. => Unless ……………………………………………………………….. 3. Unless our team had joined the competition, we would not have achieved this prize. => If ……………………………………………………………….. 4. If students don’t return books to the library this week, they’ll have to pay a fine. => Unless ……………………………………………………………….. 5. If Peter didn’t study hard, he could not get high marks. => Unless ………………………………………………………………..
Cho tam giác ABC vuông tại A, đường cao AH=30cm, biết `\frac{AB}{AC}=\frac{5}{6} `. Tính HB, HC, AB, AC? Sử dụng hệ thức về cạnh và đường cao trong tam giác vuông
Lẹ nha mk cần gấp Ai TL chích xác nhất mk cho5sao
I. Put the verbs in correct tenses. 1. _____________ you (wait) _____________ for her when her plane arrives tonight? 2. Don’t phone me between 7 and 8. We (have) _____________ dinner then. 1. I (send) _____________ you my book tomorrow. 2. We hope the new Director (find) _____________ more jobs for his employees. 3. Nam is a hard-working student. He (pass) _____________ the exam easily this year. 4. What _____________ you (do) _____________ when you graduate from the University? Next week we (have) _____________ many kinds of examinations. It (be) _____________ a very busy week, I think. 5. In the future, most of Vietnamese people (be able) _____________ (speak) _____________ English well. 6. Next week at this time, you (lie) _____________ on the beach. 7. _____________ You (meet) _____________ your former teacher at 9 am tomorrow? 8. Keep silent ! I (listen )____________________to the radio. 9. ______________ you (play)_________________badminton now? 10. Her favourite subject (be)__________________English. 11. Now, my brother (like)_________________eating bananas. 12. She (like )________________Tea, but she (not like)____________________coffee. 13. In the summer, I sometimes (go)____________________swimming. 14. Every evening, my mother (like)___________ watching television. 15. Lan (have) _______________breakfast and (go)___________to school at 6.30 a.m. 16. We (not read)___________________after lunch. 17. I ( meet) _______________you tonight. 18. He (come) _______________tomorrow. 19. We (live) _______________ there for six years now. 20. We (not visit ) _______________Don Village last summer. You (visit) there yet? _______________ 21. Yesterday I (buy) _______________a new book about allergy. 22. Hoa (be) _______________ sick since this morning. 23. My friends hate (eat) ________ out. They think it (cost) _______ a lot of money. 24. We find (arrange)_______________ flowers interesting because it (help) __________ us relax. 25. Don’t worry. I (go) _________ swimming with you tomorrow. 26. She loves _____________at the weekend (fish)
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