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Tìm lỗi sai trong các câu sau :
1. I wish this problem hadn't seem =>seemed difficult for me.
2. They have given me three bikes since I start =>started riding to school.
3. Lion King is one of the most interesting cartoon =>cartoons I have ever seen.
4. I didn't use to go swimming when I live =>lived in the countryside.
1. I haven't enjoyed myself so much since many months
=> FOR
2. This car was a completely waste of money. I wish I hadn't bought it
=> Bỏ
3. I received letter from my close friend a few days ago
=> FEW
4. They wish their house were little bigger
=> WISHED
45 minutes \(are\)not long enough for the students minute the text
\(\Rightarrow\)45 minutes aren't not long enough for the students to finish the text
Bài 1 :Tìm lỗi sai và sửa lại
36. Almost=>most American Indian cultures have been agricultural societies since 2000 BC.
37. Would you like to contribute for=>to our earthquake fund?
38. The=>x violence is a very great problem in the world.
39. Now that the stress of examinations are=>is over, we can go somewhere for our holiday
40. Passengers are advised not to leave their luggage attended=>unattended.
1.I dreamt of evil creature that were trying to catch me => was
2. The Internet is a very fast and convenient way for us to get a lot of informations => information
3. Jim's grandfather left him 50,000 dollars, this was too big a sum to him => which
1. B. use -> using
2. C. to contact -> contacting
3. D. has played -> played
4. B. although -> because
5. A. that -> which
1 B => using
2 C => contacting
3 D => played
4 B => Because
5 B => bought
8. It is very difficult for me crossing => to cross the rive at night.
A B C D
9. Lan can run the fastest=> faster than her friends.
A B C D
10. Nam is the taller => tallest boy in this school.
A B C D
11. Because of => because An's English was poor, she couldn't pass the final exam
A B C D
12.Our classroom doesn't have any windows. I wish our classroom has => had some windows
A B C D
13. Jom asked me did I like=> if I liked his new motorbike.
A B C D
14. He has learned a lot in the last couple of years, didn't => hasn't he?
A B C D
15. They don't => didn't stay at the park very long last sunday.
A B C D
16. We usually go to our home village at least once a week on => in summer.
A B C D
1. ever visit -> have ever visited
-> thì HTHT have/has ever V3/ed
2. will sit -> will be sitting
-> this time next week (thì TLTD)
3. played -> playing
-> HTHTTD : hành động xảy ra ở quá khứ, tiếp tục ở hiện tại và có thể tiếp diễn trong tương lai
4. writing -> was writing
-> when QKĐ, QKTD
5. will have -> will be having
-> from nine to ten in this room (TLTD)
6. made -> have been making
-> HTHTTD : hành động xảy ra ở quá khứ, tiếp tục ở hiện tại và có thể tiếp diễn trong tương lai, hành động đã hoàn thành nhưng kết quả vẫn ở hiện tại
7. have been speaking -> had been speaking
-> QKHTTD : hành động đã đang diễn ra, kết thúc trước một hành động khác trong quá khứ
8. stopped -> stops
-> S can't V until S Vs/es
9. had got -> got
-> các hành động liên tiếp xảy ra trong quá khứ
10. had they played -> were they playing
-> QKTD when QKĐ
I wish the problem hadn't seem => weren't dificult for me
\(P=\left(\frac{a}{a+b}\right)^4+\left(\frac{b}{b+c}\right)^4+\left(\frac{c}{c+a}\right)^4=\left(\frac{1}{1+\frac{b}{a}}\right)^4+\left(\frac{1}{1+\frac{c}{b}}\right)^4+\left(\frac{1}{1+\frac{a}{c}}\right)^4\)
Đặt \(\left\{{}\begin{matrix}\frac{b}{a}=x\\\frac{c}{b}=y\\\frac{a}{c}=z\end{matrix}\right.\) \(\Rightarrow xyz=1\)
\(P=\frac{1}{\left(1+x\right)^4}+\frac{1}{\left(1+y\right)^4}+\frac{1}{\left(1+z\right)^4}\)
Ta có \(\frac{1}{\left(1+x\right)^4}+\frac{1}{16}\ge\frac{1}{2\left(1+x\right)^2}\) tương tự với 2 biểu thức còn lại
\(\Rightarrow P+\frac{3}{16}\ge\frac{1}{2\left(1+x\right)^2}+\frac{1}{2\left(1+y\right)^2}+\frac{1}{2\left(1+z\right)^2}\)
\(\Rightarrow2P+\frac{3}{8}\ge\frac{1}{\left(1+x\right)^2}+\frac{1}{\left(1+y\right)^2}+\frac{1}{\left(1+z\right)^2}\)
Do \(xyz=1\Rightarrow\) trong 3 số luôn tồn tại ít nhất 1 số không nhỏ hơn 1, ta giả sử \(x\ge1\)
Áp dụng BĐT: \(\frac{1}{\left(1+y\right)^2}+\frac{1}{\left(1+z\right)^2}\ge\frac{1}{1+yz}\)
\(\Rightarrow2P+\frac{3}{8}\ge\frac{1}{1+yz}+\frac{1}{\left(1+x\right)^2}=\frac{x}{x+xyz}+\frac{1}{\left(1+x\right)^2}=\frac{x}{x+1}+\frac{1}{\left(1+x\right)^2}\)
\(\Rightarrow2P+\frac{3}{8}\ge\frac{x^2+x+1}{\left(x+1\right)^2}=\frac{4x^2+4x+4}{4\left(x+1\right)^2}=\frac{3\left(x+1\right)^2+\left(x-1\right)^2}{4\left(x+1\right)^2}=\frac{3}{4}+\frac{\left(x-1\right)^2}{4\left(x+1\right)^2}\ge\frac{3}{4}\)
\(\Rightarrow2P\ge\frac{3}{8}\Rightarrow P\ge\frac{3}{16}\Rightarrow P_{min}=\frac{3}{16}\) khi \(x=y=z=1\) hay \(a=b=c\)