áp dụng BĐT AM-GM

\(a^3+b^3+1\ge3ab\Rightarrow\dfrac{1}{a^3+b^3+1}\le\dfrac{1}{3ab}\)

tương tự ta có

\(\dfrac{1}{b^3+c^3+1}\le\dfrac{1}{3bc};\dfrac{1}{a^3+c^3+1}\le\dfrac{1}{3ac}\)

cộng từng vế của BĐT cho nhau

\(C\le\dfrac{1}{3ab}+\dfrac{1}{3bc}+\dfrac{1}{3ac}=\dfrac{a+b+c}{3abc}=\dfrac{a+b+c}{3}\)

mặt khác áp dụng BĐT AM-GM với 3 số a,b,c không âm

\(a+b+c\ge3\sqrt[3]{abc}=3\)

\(\Rightarrow C\le1\)

maxC=1, dấu"=" xảy ra khi a=b=c=1

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word for each of the blanks from 66 to 75.

Sudoku

Are you a fan of the popular logical puzzle that (66) x by the name Sudoku? Even if you’re not, the chances are you know somebody who is. Once (67) x known outside Japan, this addictive brain teaser has become a common feature of newspaper puzzle pages all over the world.

Sudoku’s great success (68) x much to its simplicity. The game (69) x for neither mathematical ability nor (70) x knowledge and there are just a few sentences of straightforward instructions to read before you can play. The only skill required is the ability to recognize the difference between nine different symbols, and these don’t even have to be numbers.

Some clever marketing has helped the game. Western newspapers worked hard at promoting the game. Without this, it is unlikely that it would have (71) x off and become quite such a runaway success. The same also (72) x from its Japanese name that made people in many parts of the world (73) x . It as a superior kind of puzzle compared to those you usually find in newspapers and magazines.

But the popularity of Sudoku reached a peak in 2006, if the number of (74) x on one leading website is anything to go by. Newspapers responded by (75) x up with new kinds of logical puzzles, all with simple rules and Japanese names. But for true Sudoku fans, only the real thing will do.

Điền vào ô 74

A. hits

B. clicks

C. strikes

D. shots

bình phương 2 vế lên là ra p :>

Read the following passage and mark the letter A, B, C, or D on your answer sheet to choose the word or phrase that best fits each of the numbered blanks from 17 to 26.

BURIED TREASURE

Artist Kit Williams was always interested in trying new things, so when it was suggested that he should (17)________a book, he preferred to write his own story rather than work with someone else's. He hit (18)________a

new idea . What better way to attract people's (19)________to his work than to give his readers the chance to take

part in a treasure hunt? So Kit made a golden pendant in the (20)________of a hare and buried it underground at a secret location. The words and pictures in his book, Masquerade, (21)________clues        as to where the hare was

buried. Almost two million readers from all over the world joined in the rush to solve the puzzle. The race was open to all, and no one had any advantage - the treasure was as likely to be found by a clever child of ten as it was by a university professor.

After more than two years, the golden hare was found by a businessman who called himself Ken Thomas,

although this was actually a (22)________name. It appears that “Thomas” subsequently sold the hare for a large (23)________of money. Afterwards some people (24)________that the discovery of the hare was not based purely on the information in the book, but was the result of a complex (25)________in which “Thomas” was helped by a former girlfriend of Kit Williams. However, “Thomas” has always firmly (26)________these claims.Question 20

A. appearance

B. pattern

C. shape

D. figure

Chất có trạng thái khác với các chất còn lại ở điều kiện thường là :

A. axit glutamic

B. metyl aminoaxetat

C. Alanin

D. Valin

đặt chiều rộng là a(a>0)

=>chiều dài là 40/a

ta có pt

\(\left(a+3\right)\left(\dfrac{40}{a}+3\right)=88\)

\(\Rightarrow a=5\)

\(\Rightarrow\) kích thước còn lại là 8

1)

\(\left\{{}\begin{matrix}x+y=4\\2x+3y=m\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3x+3y=12\\2x+3y=m\end{matrix}\right.\)

trừ 2 vế của pt cho nhau ta tìm được

\(\left\{{}\begin{matrix}x=12-m\\y=m-8\end{matrix}\right.\)

để \(\left\{{}\begin{matrix}x>0\\y< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m< 12\\m< 8\end{matrix}\right.\Rightarrow}m< 8}\)

dễ thấy \(\Delta=m^2-2m+1=\left(m-1\right)^2\ge0\)

\(x_1=\dfrac{3m-1+\left|m-1\right|}{2}\) ;\(x_2=\dfrac{3m-1-\left|m-1\right|}{2}\)

xét m\(\ge1\)

\(\Rightarrow x_1=2m-1;x_2=m\)

\(x_1=x_2^2\Rightarrow m=1\left(tm\right)\)

xét m\(\le1\)

\(\Rightarrow x_2=2m-1;x_1=m\)

\(x_1=x_2^2\Rightarrow\left[{}\begin{matrix}m=1\\m=\dfrac{1}{4}\end{matrix}\right.\)