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\(B=\dfrac{x-1}{\sqrt{x}-1}-\dfrac{x+3\sqrt{x}}{\sqrt{x}}\)

\(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}-\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{\sqrt{x}}\)

\(=\sqrt{x}+1-\sqrt{x}-3=-2\)

\(B=\dfrac{x-1}{\sqrt{x}-1}-\dfrac{3\sqrt{x}+x}{\sqrt{x}}\left(x>0,x\ne1\right)\\ =\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}-\dfrac{\sqrt{x}\left(3+\sqrt{x}\right)}{\sqrt{x}}\\ =\sqrt{x}+1-\left(\sqrt{x}+3\right)\\ =\sqrt{x}+1-\sqrt{x}-3\\ =-2\)

\(\text{Δ}=\left(-6\right)^2-4\cdot1\cdot\left(-m\right)=4m+36\)

Để phương trình có hai nghiệm phân biệt thì Δ>0

=>4m+36>0

=>m>-9

Theo Vi-et, ta có:

\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=6\\x_1x_2=\dfrac{c}{a}=-m\end{matrix}\right.\)

\(\left(x_1-x_2\right)^2=\left(x_1+x_2\right)^2-4x_1x_2=36+4m\)

=>\(x_1-x_2=\pm2\sqrt{m+9}\)

\(x_1^2-x_2^2=24\)

=>\(\left(x_1+x_2\right)\left(x_1-x_2\right)=24\)

=>\(\pm2\sqrt{m+9}=4\)

=>\(\pm\sqrt{m+9}=2\)

=>\(\left[{}\begin{matrix}\sqrt{m+9}=2\left(nhận\right)\\\sqrt{m+9}=-2\left(loại\right)\end{matrix}\right.\Leftrightarrow m+9=4\)

=>m=-5(nhận)

\(\left\{{}\begin{matrix}x^2+y^2+2x=4\\x+2y+xy=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2+y^2+2x=4\\2x+4y+2xy=8\end{matrix}\right.\)

\(\Rightarrow x^2+y^2+2x+2x+4y+2xy=12\)

\(\Leftrightarrow\left(x+y\right)^2+4\left(x+y\right)-12=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+y=2\\x+y=-6\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}y=2-x\\y=-6-x\end{matrix}\right.\)

TH1: \(y=2-x\). Thế vào pt thứ 2 của hệ, ta có:

\(x+2\left(2-x\right)+x\left(2-x\right)=4\)

\(\Leftrightarrow x+4-2x+2x-x^2-4=0\)

\(\Leftrightarrow x-x^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\Rightarrow y=2\\x=1\Rightarrow y=1\end{matrix}\right.\)

TH2: \(y=-x-6\). Thay vào pt thứ 2 của hệ, ta có:

\(x+2\left(-x-6\right)+x\left(-x-6\right)=4\)

\(\Leftrightarrow x-2x-12-x^2-6x-4=0\)

\(\Leftrightarrow-x^2-7x-16=0\) (vô nghiệm vì \(-x^2-7x-16< 0\) với mọi \(x\))

Vậy hệ phương trình đã cho có 2 cặp nghiệm \(\left(x;y\right)\) là \(\left(1;1\right)\) và \(\left(0;2\right)\)

Read the following passage and mark the letter A, B, C or D to indicate the correct answer to each of the questions.

Travel is something which people do every day. It may be a trip to school, university or to work. Travelling can often take a long time, especially when great distances need to be covered. People often enjoy travelling abroad for holidays. But for some people travelling is not fun at all. Some people suffer from travel sickness. This means that they will become very unwell each time they travel.
Travelling can be either affordable or costly. It often depends on how far you want to travel and the choice of transport.
- Using a bicycle will not cost anything as you power it by using your legs. However, the use of a bicycle can be hard work and can take a lot of time to travel long distances.
- Cars and motorcycles are faster modes of transport, but are more expensive to use as gasoline is needed for them to work. It can usually be assumed that the longer you wish to travel, the more expensive and time consuming it will be.
- The use of a plane is necessary for people wanting to travel very long distances. A pilot will fly a plane from an airport for many thousands of miles to take people to places far away. Although traffic is rarely a problem for airplanes, it can take a lot of preparation to travel by plane.
- A train is another mode of transport which is ideal for travelling long distances within the same country, or between countries which are connected by land. A train driver will stop at train stations on route to allow passengers wishing to proceed to the scheduled destination to board the train.
- A number of destinations can be travelled to by using the sea. People often depart from a harbour in a ferry which is driven by a captain. If the journey is a long distance, people may choose to sleep on the ferry while they wait to arrive at their destination. Some people choose to go on a cruise for their holiday, which would involve stopping at many different city ports for a short amount of time.
- People who need to travel short distances may choose not to use any transport at all. People often rely on their legs to take them to places nearby.

Question 36. Why do some people not enjoy travelling?

A. It’s expensive

B. They find it a waste of time

C. They have trouble with their health

D. It isn’t comfortable

Question 37. According to the passage, you don’t have to pay any money when you ________.

A. fly with a plane and catch a bus

B. take a train and a taxi

C. use a bicycle and motorbike

D. go on foot and ride a bicycle

Question 38. Passengers have to prepare a lot of things when travelling by.

A. train B. plane C. bus D. ferry

Question 39. Which means of transport is ideal for travelling between countries connected by land?

A. car B. airplane C. bicycle D. train

Question 40. If people travel by _________, they can go on a voyage or a cruise for their holiday.

A. ocean B. sea C. air D. land

Question 9. Our team leader suggested that we ______________ a show to raise money for poor people in the village.

A. to organize B. organizing C. organize D. organized

Question 10. One of the attractions in my hometown is the traditional market ______________ is open every Sunday.

A. whose B. whom C. which D. who

Question 11. ______________ energy can be easily used in tropical countries where there is a lot of sunlight.

A. Fossil fuel B. Nuclear C. Solar D. Wind

Question 12. We will live a happier and healthier life ______________ we keep our environment clean.

A. however B. although C. unless D. if

Question 13. Ha Noi, the capital of Viet Nam, has a (n) ______________ of over 8 million people.

A. growth B. climate C. area D. population

Question 14. Television can ______________ people with the latest information in an inexpensive and convenient way.

A. communicate B. provide C. apply D. interact

Question 15. Our lives ______________ since the invention of the Internet.

A. will be improved B. was improving C. have been improved D. be improved

Question 16. The journalist posted this article on the website yesterday, ______________?

A. don’t they B. didn’t he C. didn’t they D. doesn’t he

Question 17. The university has an international ______________ for academic excellence.

A. tuition B. knowledge C. reputation D. edition

Question 18. I wish my sister ______________ harder for her examination.

A. has worked B. will work C. worked D. works

#\(yGLinh\)

Lời giải:
Áp dụng BĐT Bunhiacopxky:

$(\sqrt{2a+b}+\sqrt{2b+c}+\sqrt{2c+a})^2\leq [(2a+b)+(2b+c)+(2c+a)](1+1+1)=3(a+b+c).3=9(a+b+c)=81$

$\Rightarrow \sqrt{2a+b}+\sqrt{2b+c}+\sqrt{2c+a}\leq 9$

Vậy ta có đpcm

Dấu "=" xảy ra khi $a=b=c=3$

\(\dfrac{1}{2}\left(x+1\right)\left(3-x\right)+x=3\)

\(\Leftrightarrow\left(\dfrac{1}{2}x+\dfrac{1}{2}\right)\left(3-x\right)-\left(3-x\right)=0\)

\(\Leftrightarrow\left(3-x\right)\left(\dfrac{1}{2}x+\dfrac{1}{2}-1\right)=0\)

\(\Leftrightarrow\left(3-x\right)\left(\dfrac{1}{2}x-\dfrac{1}{2}\right)=0\)

\(\Leftrightarrow\dfrac{1}{2}\left(3-x\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3-x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

Vậy phương trình đã cho có tập nghiệm là \(S=\left\{3;1\right\}\).

$Toru$

\(\dfrac{1}{2}\left(x+1\right)\left(3-x\right)+x=3\)

=>\(\dfrac{1}{2}\left(3x-x^2+3-x\right)+x=3\)

=>\(\dfrac{1}{2}\left(-x^2+2x+3\right)+x=3\)

=>\(-x^2+2x+3+2x=6\)

=>\(-x^2+4x-3=0\)

=>\(\left(x-1\right)\left(x-3\right)=0\)

=>\(\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)

Hình vẽ đâu bạn ơi?

x-y=4

=>y=x-4

Vậy: Nghiệm tổng quát là \(\left\{{}\begin{matrix}x\in R\\y=x-4\end{matrix}\right.\)

Biểu diễn nghiệm: