\(A=5x^2+2y^2+2xy-26x-16y+54\) \(=2\left(y^2+y\left(x-8\right)+\dfrac{\left(x-8\right)^2}{2}\right)-\dfrac{\left(x-8\right)^2}{2}+5x^2-26x+54\)

\(=2\left(y+\dfrac{x-8}{2}\right)^2+\dfrac{9}{2}x^2-18x+22\)

\(=2\left(y+\dfrac{x-8}{2}\right)^2+\dfrac{9}{2}\left(x-2\right)^2+4\ge4\)

Dấu '' = '' xảy ra khi: \(\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\y+\dfrac{x-8}{2}=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)

Vậy: Min A = 4 tại \(x=2;y=3.\)

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

If the salinity of ocean waters is analyzed, it is found to vary only slightly from place to place. Nevertheless, some of these small changes are important. There are three basic processes that cause a change in oceanic salinity. One of these is the subtraction of water from the ocean by means of evaporation-conversion of liquid water to water vapor. In this manner, the salinity is increased, since the salt behind. If this is carried to the extreme, of course, white crystals of salt would be left behind.

The opposite of evaporation is precipitation, such as rain, by which water is added to the ocean. Here the ocean is being diluted so that the salinity is decreased. This may occur in areas of high rainfall or in coastal regions where rivers flow into the ocean. Thus salinity may be increased by the subtraction of water by evaporation, or decreased by the addition of fresh water by precipitation or runoff.

Normally, in tropical regions where the sun is very strong, the ocean salinity is somewhat higher than it is in other parts of the world where there is not as much evaporation. Similarly, in coastal regions where rivers dilute the sea, salinity is somewhat lower than in other oceanic areas.

A third process by which salinity may be altered is associated with the formation and melting of sea ice. When seawater is frozen, the dissolved materials are left behind. In this manner, seawater directly beneath freshly formed sea ice has a higher salinity than it did before the ice appeared. Of course, when this ice melts, it will tend to decrease the salinity of the surrounding water.

In the Weddell Sea, off Antarctica, the densest water in the ocean is formed as a result of this freezing process, which increases the salinity of cold water. This heavy water sinks and is found in the deeper portions of the oceans of the world.

The word “it” in paragraph 4 refers to .

A. sea ice 

B. manner 

C. seawater 

D. salinity 

Hai cực của pin điện hoá được ngâm trong chất điện phân là dung dịch

A. muối           

B. axit 

C. bazơ            

D. một trong các dung dịch trên

Đặt: \(x+\dfrac{1}{x}=t\)

\(x^2+\dfrac{1}{x^2}=t^2-2\) \(\)

Ta có: \(18\left(x+\dfrac{1}{x}\right)^2+9\left(x^2+\dfrac{1}{x^2}\right)^2-9\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=\left(x+2\right)^2\)

\(\Leftrightarrow\) \(18t^2+9\left(t^2-2\right)^2-9t^2\left(t^2-2\right)=\left(x+2\right)^2\)

\(\Leftrightarrow\) \(18t^2+9t^4-36t^2+36-9t^4+18t^2=\left(x+2\right)^2\)

\(\Leftrightarrow\) \(\left(x+2\right)^2=36\)

\(\Leftrightarrow\) \(\left[{}\begin{matrix}x+2=6\\x+2=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)

Vậy: Tổng tất cả các nghiệm của phương trình: \(18\left(x+\dfrac{1}{x}\right)^2+9\left(x^2+\dfrac{1}{x^2}\right)^2-9\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=\left(x+2\right)^2\) là \(-8+4=-4\) .

\(\dfrac{S_{MNP}}{S_{ABC}}=\dfrac{61}{1} \)

Sử dụng định lý Ta-lét là ra thôi

Ta có: \(\dfrac{1}{x^2-4}=\dfrac{a}{x-2}+\dfrac{b}{x+2}\Rightarrow\dfrac{1}{x^2-4}=\dfrac{ax+2a+bx-2b}{x^2-4}\)

\(\Rightarrow ax+2a+bx-2b=1\)

\(\Rightarrow x\left(a+b\right)+\left(2a-2b\right)=0x+1\)

\(\Rightarrow\left\{{}\begin{matrix}a+b=0\\2a-2b=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=\dfrac{1}{4}\\b=-\dfrac{1}{4}\end{matrix}\right.\)

Vậy: \(a=\dfrac{1}{4};b=-\dfrac{1}{4}\).

Đặt: \(a-b=x\)

\(a-c=y\)

\(b-c=z\)

Ta có: \(A=\dfrac{1}{\left(a-b\right)\left(a-c\right)}+\dfrac{1}{\left(b-a\right)\left(b-c\right)}+\dfrac{1}{\left(c-a\right)\left(c-b\right)}\)

\(=\dfrac{1}{xy}-\dfrac{1}{xz}+\dfrac{1}{yz}\)

\(=\dfrac{xyz^2-xy^2z+x^2yz}{x^2y^2z^2}\)

\(=\dfrac{xyz\left(z-y+x\right)}{x^2y^2z^2}\)

\(=\dfrac{z-y+x}{xyz}\)

Thay \(a-b=x;a-c=y;b-c=z\) vào biểu thức \(\dfrac{z-y+x}{xyz}\), ta được:

\(\dfrac{\left(b-c\right)-\left(a-c\right)+\left(a-b\right)}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}\)

= \(\dfrac{b-c-a+c+a-b}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}\)

= 0

Vậy:\(A=\dfrac{1}{\left(a-b\right)\left(a-c\right)}+\dfrac{1}{\left(b-a\right)\left(b-c\right)}+\dfrac{1}{\left(c-a\right)\left(c-b\right)}=0\)

có \(A=-\left[\left(2x\right)^2-2.2x.\frac{1}{2}+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2-5\right]\)

\(=-\left[\left(2x-\frac{1}{2}\right)^2-\frac{21}{4}\right]=-\left(2x-\frac{1}{2}\right)^2+\frac{21}{4}\ge\frac{21}{4}\)

Vậy Min A = \(\frac{21}{4}\) khi đó \(-\left(2x-\frac{1}{2}\right)^2=0\Rightarrow\left(2x-\frac{1}{2}\right)^2=0\Rightarrow2x-\frac{1}{2}=0\Rightarrow2x=\frac{1}{2}\Rightarrow x=\frac{1}{4}\)