Which sentence is CORRECT?
1. A. If he call, let me know.
B. Should he call, let me know.
C. Would he call, let me know.
2. A. Were they to escape, there would be an outcry.
B. Were they escaping, there would be an outcry.
C. Were they escaped, there would be an outcry.
3. A. If I had know, I would have protested strongly.
B. Had I known, I would have protested strongly.
C. Was I to have known, I would have protested strongly.
4. A. Scarcely had it stopped raining than the sun came out.
B. No sooner had it stopped raining than the sun came out.
C. No sooner it had stopped raining than did the sun come out.
5. A. Not until did the mother come home that the boy stop crying.
B. Not until the mother came home that did the boy stop crying.
C. It was not until the mother came home that the boy stop crying.
6. A. Such the force of the storm was that trees were uprooted.
B. So was the force of the storm that trees were uprooted.
C. So much was the force of the storm that trees were uprooted.
7. A. Only by searching the Internet for the keys did he finish the homework.
B. By searching the Internet for the keys did he finish the homework.
C. Only by searching the Internet for the keys did he finished the homework.
8. A. Never have I seen this kind of creature before.
B. Never I have seen this kind of creature before.
C. Never do I see this kind of creature before.
9. A. Suddenly came down the rain!
B. Suddenly down came the rain!
C. Suddenly down did the rain come!
10. A. Difficult though it may be, it is not impossible.
B. Difficult although it may be, it is not impossible.
C. Difficult even though it may be is it not impossible.
11. A. Rarely do I have so much responsibility.
B. Rarely don’t I have so much responsibility.
C. Rarely do I not have so much responsibility.
12. A. Little the government appreciate what the results will be.
B. Little do the government appreciate what the results will be.
C. Little the government appreciates what the result will be.
13. A. Only Mary realized that the door was not locked.
B. Only Mary did realize that the door was not locked.
C. Only did Mary realize that the door was not locked.
14. A. At no time I was aware of anything out of the usual.
B. At no time was I aware of something out of the usual.
C. At no time was I aware of anything out of the usual.
15. A. In no condition are they to open fire without a warning.
B. At no condition are they to open fire without a warning.
C. On no condition are they to open fire without a warning.
16. A. Not only he sings well but he also plays musical instruments perfectly.
B. Not only does he sing well but he also plays musical instruments perfectly.
C. Not only he sings well but does he also play musical instruments perfectly.
17. A. In any way can the bus driver be blamed for the accident.
B. In no way can the bus driver not be blamed for the accident.
C. In no way can the bus driver be blamed for the accident.
18. A. On no account will I lend you the money.
B. On any account will I lend you the money.
C. In no account will I lend you the money.
19. A. Abby said that under no circumstances could Abby go out with her pals.
B. Abby said that under no circumstances Abby could go out with her pals.
C. Abby said that under no circumstances could Abby have gone out with her pals.
20. A. Not since 1994 anyone has won so many matches for his team.
B. Since 1994 no one hasn’t won so many matches for his team.
C. Not since 1994 has anyone won so many matches for his team.
We have:\(\hept{\begin{cases}a^2+b^2+c^2=\frac{1}{3}\\a,b,c>0\end{cases}\Rightarrow0< a,b,c< \frac{1}{\sqrt{3}}}\)
We prove to:
\(4x+\frac{2}{3x}\ge-3x^2+\frac{11}{3}\) with \(0< x< \frac{1}{\sqrt{3}}\)
\(\Leftrightarrow4x+\frac{2}{3x}+3x^2-\frac{11}{3}\ge0\)
\(\Leftrightarrow9x^3+12x^2-11x+2\ge0\)
\(\Leftrightarrow\left(3x+1\right)^2\left(x+2\right)\ge0\) Always true to all \(0< x< \frac{1}{\sqrt{3}}\)
\(\Rightarrow VT\ge-3a^2+\frac{11}{3}-3b^2+\frac{11}{3}-3c^2+\frac{11}{3}\)
\(=-3\left(a^2+b^2+c^2\right)+11=-3.\frac{1}{3}+11=10\) \(\left(đpcm\right)\)
Đặt biểu thức trên là \(A\)
Ta có : \(A=\left(4a+\frac{2}{3a}\right)+\left(4b+\frac{2}{3b}\right)+\left(4c+\frac{2}{3c}\right)\)
Cần chứng minh \(4a+\frac{2}{3a}\ge-3a^2+\frac{11}{3}\) (*)
Thật vậy \(BĐT\Leftrightarrow4a+\frac{2}{3a}+3a^2-\frac{11}{3}\ge0\)
\(\Leftrightarrow\frac{12a^2+2+9a^3-11a}{3a}\ge0\Leftrightarrow\frac{\left(a+2\right)\left(3a-1\right)^2}{3a}\ge0\) (luôn đúng)
Tương tự : \(4b+\frac{2}{3b}\ge-3b^2+\frac{11}{3}\) và \(4c+\frac{2}{3c}\ge-3c^2+\frac{11}{3}\)
Cộng các bất dẳng thức vừa CM đc ta có :
\(A\ge-3\left(a^2+b^2+c^2\right)+\frac{11}{3}.3=-3.\frac{1}{3}+11=10\)
Dấu "=" xảy ra \(\Leftrightarrow a=b=c=\frac{1}{3}\)