Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
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 \(a=b=c\)
Tham khảo
Câu 5 :
1. wish wishes
2. rained rain
3. was were
4. have had
5. didnt rain hadnt rain
6. gives would give
7. studied had studied
8. will would
9. stops stopped
10. are were
11. is - were
12. will would
13. am were
14. been be
15. wish wishes
Câu 6 :
1. I wish I didnt have to study.
2. I wish we hadnt had a lot of homework yesterday.
3. I wish it didnt rain heavily.
4. I wish it hadnt been cold last night.
5. I wish they didnt work slowly.
6. I wish I were good at English.
7. I wish he didnt studied badly.
8. I wish he liked playing sports.
9. I wish I had a computer.
10. I wish today were a holiday.
11. I wish I could sing this song.
12. I wish he hadnt been punished by his mother.
13. I wish they would come here again.
14. I wish I he would go swimming with me.
15. We wish we had understood them.
16. I wish I wouldnt be late for school.
17. I wish the bus hadnt been late today.
18. I wish she liked this place.
19. I wish these students hadnt talked too much in class.
20. I wish I could play basketball.
1 could => can
2 rained => rain
3 was => were
4 have => had
5 didn't rain => hadn't rained
6 gives => would give
7 studied => had studied
8 will => would
9 stops => stopped
10 are => were
11 is => were
12 will => would
13 am => were
14 been => be
15 wish => wishes
1 could => can
2 rained => rain
3 was => were
4 have => had
5 didn't rain => hadn't rained
6 gives => would give
7 studied => had studied
8 will => would
9 stops => stopped
10 are => were
11 is => were
12 will => would
13 am => were
14 been => be
15 wish => wishes
Đáp án: D
Đã dùng đại từ quan hệ thay thế tân ngữ nên không cần “her” nữa
Dịch: Sáng nay, tôi đã gặp người bạn học cũ Janet, người mà tôi đã gặp từ lâu.
1 like => as
2 hard => as hard
3 different => different from
4 as => bỏ
5 the same => as
6 as => drom
7 like => as
8 length => long
9 than => as
10 is => has
1, Lỗi sai ở : Or -> They don't have any fruits and vegetables.
2. Lỗi sai ở : Who's -> Whose shirt is this?
tả lời Cả Câu nay hộ tớ nha Students in the USA often(not wear)sChool uniform
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.